United States Office of EPA 520/1-87-024-1
Environmental Protection Radiation Programs December 1987
Agency Washington, D.C. 20460
Radiation
v>EPA Low-Level and NARM
Radioactive Wastes
Model Documentation
PRESTO-EPA-POP .
Volume 1
Methodology Manual
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40 CFR Part 193 EPA 520/1-87-024-1
Environmental Radiation Standards (RAE 8706/1-1)
for Management and Land Disposal
of Low-Level Radioactive Wastes
PRESTO-EPA-POP: A Low-Level Radioactive Waste Environmental
Transport and Risk Assessment Code
Volume 1
METHODOLOGY MANUAL
Developed by
D. E. Fields
C.A. Little
Fidel Parraga
Vern Rogers
Cheng Hung
December 1987
Prepared for
U.S. Environmental Protection Agency
Office of Radiation Programs
Washington, DC 20460
Cheng Hung, Project Officer
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DISCLAIMER
The report was prepared as an account of work sponsored by an agency
of the United States Government. Neither the United States Government nor
any agency thereof, nor any of their employees, contractors, subcontractors,
or their employees, makes any warranty, express or implied, nor assumes any
legal liability or responsibility for any third party's use of the results
of such use of any information, apparatus, product or process disclosed in
this report, nor represents that its use by such third party would not
infringe privately owned rights.
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PREFACE
Tnis two-volume PRESTO-EPA-POP model documentation provides
the background information on the mathematical modeling used to
generate the basic data for the Environmental Impact Statement
( E I S ) which is used to support EPA's rulemaking for generally
applicable environmental standards for the management and
disposal of low-level radioactive wastes (Llw). Volume 1 of the
PRESTO-EPA-POP documentation presents the theoretical bases of
the mathematical model and their implemented computer code for
the assessment of the cumulative population health effects
(including fatal cancer deaths and serious genetic effects) to
the general population residing in th.e downstream regional basin
of a LLW disposal site. The model simulates the leaching of
radionuc1ides from the waste matrix, the hydro logical,
hydrogeo1ogica1, ana biological transports, the resultant human
exposures, and finally the assessment of the probable health
effects for the entire regional water basin population. Volume
2 of the PRESTO-EPA-POP documentation provides the information
on the structure of the computer code and how it is used in the
health effects assessments.
The two volumes present enough model detail so that
interested persons may apply the model, using appropriate and
applicable input data, for assessing the cumulative population
health effects from a LLW disposal site.
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TABLE OF CONTENTS
Page
LIST OF FIGURES vii
LIST OF TABLES viii
EXECUTIVE SUMMARY ix
1 INTRODUCTION 1-1
1.1 Description of a Low-Level Waste Disposal Site . . . 1-1
1.2 Description of Model 1-7
1.3 Outline of Methodology Manual 1-12
2 DISCUSSION OF METHODOLOGY 2-1
2.1 Environmental Transport Pathways 2-1
2.1.1 Transport Pathways Involving Water 2-4
2.1.2 Atmospheric Transport Sources and Pathways . 2-24
2.1.3 Food Chain Calculations 2-34
2.2 Dose and Health Effect Calculations 2-44
2.2.1 DARTAB Calculations 2-44
2.2.2 Estimation of Basement Dose to Resident
Intruder 2-49
2.2.3 Accounting for Radioactive Decay Products . . 2-56
2.3 Health Effects to Regional Basin Population .... 2-57
2.3.1 Calculations of Regional Basin Health Effects 2-60
2.3.2 Conversion Factors for Regional Basin Health
Effects 2-63
3 DEVELOPMENT OF PRESTO-EPA-POP CODE 3-1
3.1 Structure and Information Flow 3-1
3.2 Subroutine Description 3-3
4 DESCRIPTION OF OUTPUT OF THE PRESTO-EPA-POP CODE .... 4-1
4.1 Replication of Input Data 4-1
4.2 Organization of Input Data 4-1
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TABLE OF CONTENTS
(Continued)
Page
4.3 Radionuclide Summary Tables
4.4 INFIL Input/Output
4.5 Unit Response Calculations
4.6 Annual Summary Tables for Specified Years . . .
4.7 Radionuclide Concentration Tables
4.8 Radionuclide Exposure Tables
4.9 DARTAB Control Information
4.10 DARTAB Dose Tables
4.11 DARTAB Fatal Cancer Risk Tables
4.12 Residual Radioactivity Released to the Basin and
Health Effects
4-3
4-4
4-4
4-4
4-5
4-5
4-6
4-6
4-6
4-7
REFERENCES
R-l
APPENDIX A - A MODEL TO SIMULATE INFILTRATION OF RAINWATER
THROUGH THE COVER OF A RADIOACTIVE WASTE TRENCH
UNDER SATURATED AND UNSATURATED CONDITIONS . . ,
A-l
APPENDIX B - AN OPTIMUM GROUNDWATER TRANSPORT MODEL FOR
APPLICATION TO THE ASSESSMENT OF HEALTH EFFECTS
DUE TO LAND DISPOSAL OF RADIOACTIVE WASTES . . .
B-l
APPENDIX C - RADE MODEL: A RADIOACTIVE ATMOSPHERIC DISPERSION
AND EXPOSURE CODE
C-l
VI
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LIST OF FIGURES
Figure No. Page
1-1 Environmental Transport Pathways Used in PRESTO-EPA-POP . 1-4
2-1 Hydro!ogic Environmental Transport Pathways 2-2
2-2 Atmospheric Environmental Transport Pathways 2-3
2-3 Trench Cap Removal Function 2-11
2-4 Regional Basin Health Effects Pathway 2-59
3-1 PRESTO-EPA-POP Subroutine Structure 3-2
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LIST OF TABLES
Table No.
Page
1-1 PRESTO-EPA Code Family ................. 1-2
1-2 Radiological Exposure Pathways for Selected Scenarios . . 1-13
2-1 Leaching Options Specified by LEAOPT .......... 2-13
2-2 Units of Exposure Factor, E-JJ, and Dose Rate Factor,
DF-j -ji , for Selected Individual Dose Rate Calculations by
DARTAB ......................... 2-46
2-3 Units of Years Lost Factor, YLj j-| , and Mortality Risk
Factor, RF-,- j-| , for Health Risk Calculations by DARTAB . . 2-50
2-4 Results of Basement and Infinite Plane Unit Dose Rate
Computations ...................... 2-55
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EXECUTIVE SUMMARY
The U.S. Environmental Protection Agency (EPA) is responsible for
developing a generally applicable standard for the land disposal of
low-level radioactive waste (LLW). As an aid in developing the standard, a
family of computer codes, entitled PRESTO-EPA-POP, PRESTO-EPA-DEEP,
PRESTO-EPA-CPG, PRESTO-EPA-BRC and PATHRAE-EPA, has been developed under EPA
direction. The PRESTO-EPA-POP code was the first code developed and served
as the basis for the other codes in the PRESTO-EPA family. PRESTO-EPA-POP
estimates potential health effects to local and regional basin populations
from the shallow land disposal of low-level radioactive waste under a wide
variety of hydrologic, geologic, climatic, site engineering, and waste form
conditions. The EPA uses the PRESTO-EPA code family to compare the
potential health impacts of a broad number of LLW disposal alternatives to
evaluate and support its decisions for the LLW standard.
In developing the LLW standard, EPA initially identified more than 24
distinct types of radioactive waste in various waste forms and containers
which required disposal by one or more of eight alternative disposal
methods within the United States. Basic requirements for the PRESTO-EPA
code family included: (1) use of existing release and pathway models where
possible to reduce development time and costs; (2) use of modular
subroutines to allow the use of improved or more appropriate submodels when
available or needed; (3) ability to rapidly and economically execute the
code for several thousand scenarios or alternatives as necessary;
(4) flexibility to analyze a wide range of hydrologic, climatic, waste
type, and site engineering combinations; (5) use of EPA's health risk
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calculational methodology; and (6) results which are reasonably realistic,
reliable, and verifiable.
The user of the PRESTO-EPA-POP code, may, with appropriate input data,
simulate a specific waste type (e.g., LWR decontamination resins), a
specific form for the waste (e.g., solidified in cement), and special
containers (e.g., 300 year high-integrity containers). The user may also
simulate special site engineering and waste emplacement configurations such
as sanitary landfill, use of deeper trenches, or installation of trench
caps with either natural or special low permeability obtained from use of
clays and compaction. Although most shallow LLW disposal facilities
consist of many disposal trenches, the PRESTO-EPA-POP code treats all LLW
trenches and their wastes as a single, representative, combined trench and
volume of wastes.
Water, principally from precipitation, is the primary agent of release
and transport of radioactivity from LLW disposed in shallow trenches.
Geology, hydrology, and climate also affect not only the mode and rate of
release, but also which transport pathways dominate, and the rate of
transport. Therefore, the input data portion of the PRESTO-EPA-POP code
and the release and transport subroutines, have been designed with
sufficient flexibility to accommodate varying hydrologic and climatic
conditions, ranging from typical conditions found in the humid southeastern
United States to the arid southwest, with reasonable accuracy and realism.
The PRESTO-EPA-POP code can simulate the following typical water-
related release and transport phenomena. Precipitation falling on the
ground surface above the trench is apportioned between infiltration into
the trench through the trench cap, drainage away from the site by surface
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runoff, and evaporation into the atmosphere. The user can specify the time
and percent of trench cap failure, and the time duration of container
integrity. Radionuclides released from the waste by infiltrated water are
transported away from a LLW disposal trench primarily by groundwater or
surface runoff. The amount of groundcover, length and steepness of the
slope, etc., and runoff percent can be specified to simulate erosion of the
surface soil and the trench cap. Radioactively contaminated water
exfiltrating into the subtrench soil zone may ultimately enter an aquifer.
Radionuclides that reach the aquifer will be transported horizontally
within the aquifer. These radionuclides will generally be transported at a
slower rate than the ground water velocity in the aquifer due to
hydrological and geochemical interaction with the solid materials in the
aquifer which retards nuclide migration. Some of the radionuclides which
enter the aquifer may eventually reach irrigation or water supply wells or
surface streams, and thus become available for uptake by the local
population. Residual radionuclides in the aquifer which are not consumed
by the local population are assumed to undergo further transport to a large
downgradient population (referred to as the "basin" population). Health
effects to the basin population are calculated for a time period of up to
10,000 years.
The overflow of contaminated water from the trench onto the surface
soil is simulated when conditions suitable for overflow occur. Once
overflow has occurred, the radionuclides are transported by surface runoff
into nearby streams and may become available for human consumption via
irrigation or drinking water. Residual radionuclides in the streams which
are not consumed during the "local" 1,000 year assessment are assumed to be
released to the regional basin within one year.
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The exposure of the local population to radionuclides transported from
LLW sites by the atmospheric pathway is also simulated. The atmospheric
transport calculations nominally assume that the local population resides
within a single 22.5-degree sector. User specified parameters give the
fraction of the year that the wind blows in that sector. A simple external
model not contained in the PRESTO-EPA codes (see Appendix C) enables the
user to make downwind atmospheric concentration calculations which properly
distributes atmospheric contamination to population centers throughout a
360 degree circle around the site.
Radionuclides remaining on the soil surface by trench overflow,
spillage during disposal operations, or erosion of the trench cap, may
become suspended in the atmosphere and transported downwind where the
nuclides may be inhaled or deposited on vegetation and soil. When the
radioactivity is deposited, the PRESTO-EPA-POP code simulates both external
exposure to humans and internal exposure from the ingestion of contaminated
crops, meat, and mil k.
The PRESTO-EPA-POP code allows the user to select special human exposure
scenarios such as an inadvertent intruder residing on or farming the site,
as well as routine migration of radionuclides from the trench through the
hydrologic and atmospheric environmental pathways to crops and drinking
water. Normal scenarios assume that the population resides downstream of
the plume of contamination and ingests radiorvuclides from various hydrologic,
atmospheric, and food chain pathways. Processes considered in calculating
individual or population exposure include: groundwater transport under
saturated or partially saturated flow conditions, surface runoff, trench
water overflow and seepage, geochemical exchange, trench cap erosion, stream
dilution, and resuspension and atmospheric dispersion of contaminated soil.
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Average annual concentrations of each radionuclide in environmental
media (e.g., well water or the atmosphere) over the assessment period are
used to calculate radionuclide concentrations in foodstuffs. Information
from foodstuffs and human ingestion and breathing rates are utilized to
calculate the annual average intake of radionuclides per individual in the
population by ingestion and inhalation. These intake data are used by the
DARTAB subroutine to estimate dose rates, health effects, and genetic
effects.
The PRESTO-EPA-POP code calculates doses, fatal health effects, and
serious genetic effects for individuals and local populations over the
period of assessment, using a lifetable approach developed by EPA. This
approach assumes that each person in the population is a member of a large
population cohort that is exposed to constant, averaged radionuclide
concentration levels. Each member of the population is assumed to ingest
regional average quantities of food (vegetables, beef, and milk) and
water. It is assumed these foods are produced on contaminated fields and
spray irrigated with contaminated water. Beef and milk cattle are also
assumed to drink contaminated water.
As previously mentioned, the PRESTO-EPA-POP code also addresses on,
request, special exposure and pathway scenarios for inadvertent intruders
residing on or farming the site. The inadvertent resident intruder scenario
assumes that an intruder unknowingly excavates a basement in the disposal
trench while building a residence. The individual is externally exposed to
the buried radionuclides because the walls of the basement of the residence
are assumed to be surrounded by trench material. The time of residency
during the assessment period when the residence is first occupied and the
xiii
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composition of the initial trench inventory which contributes to exposure
are specified by the user.
Farming the site after loss of institutional control is also treated
as a separate intrusion scenario. By farming the site, the farmer is
affected by the transport processes previously described. In contrast to
an off-site population, however, the farmer may ingest crops whose roots
have penetrated into the radioactive waste in the trench. The water used
by the farmer for irrigation and drinking normally would contain a much
higher concentration of radioactivity than water used by the off-site
population because the water is taken from a well, stream, or pond
immediately adjacent to the disposal trench. Farming activities may also
mechanically suspend contaminated soil into the atmosphere. The time when
mechanical suspension of the surface soil is initiated by farming is
specified by the user. The impact of such mechanical suspension is
calculated for both the farmer and the downwind population.
The PRESTO-EPA-POP code can be used to make health effect assessments
for up to 10,000 years following the end of the disposal operations for the
regional basin population. These assessments are made in two stages. The
first stage calculates the health effects to the local population for up to
1000 years, and the second stage calculates the health effects to the
regional basin population over 10,000 years, using a synthesized model
community in the basin. If necessary, the local assessment period, which
is a more detailed analysis, can be extended for several thousand years or
more, but with a significant increase in computer time and costs.
The health effects to the basin population are based on the
cumulative residual radionuclides leaving the disposal area with the
XIV
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surface water or groundwater. Residual radioactivity is calculated, taking
into account the time required for the radionuclides to flow through the
aquifer from the local use point to the basin stream, by considering the
amount of contaminated water consumed or used by the local community during
the period for local impact assessment and the dilutions to the basin
stream by contributions from surface runoff and stream flow coming from
upstream of the basin use point. After 1,000 years, the local community is
assumed to be incorporated in the regional basin community and the uptake
of radionuclides takes place at the regional basin.
The end of LLW disposal operations at a site is the starting time for
the assessments made by the code. The user specifies the length of time
for the local assessment period, up to 1,000 years. The regional basin
assessment period is optionally set equal to the local assessment period or
the local assessment period plus 9,000 years. For the local assessment,
subtotals for the releases to surface water, well, and atmosphere may be
calculated and printed at a number of user-specified time intervals within
the assessment period. EPA normally determines releases every 100 years
for a standard 1,000 year run. Health effects for the local population are
averaged over the length of the entire local assessment period.
The time step for the PRESTO-EPA-POP code is fixed at one year and
default, parameters in the model give annual averages. The maximum
concentration of each radionuclide and the year of the maximum for each
nuclide is printed out for the concentrations in the atmosphere, well, and
stream.
Other features in the PRESTO-EPA-POP model and code include:
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The radionuclide inventory modeled accounts for radioactive
decay during disposal operations.
The leaching of radionucl ides from the trench waste materials
can be delayed by containment in high integrity waste con-
tainers if specified by the user.
In-growth of radiological daughter products is not
calculated explicitly by the model, but can be estimated by
considering the daughters in the initial trench inventory
for some nuclides.
The sorption and desorption characteristics of each radio-
nuclide in the waste, the surface soil, the geologic disposal
media, and the underlying aquifer can be calculated by a
linear model characterized by four distribution coefficients,
or Kj values.
Groundwater flow in the host soil and disposal medium may "be
either saturated or partially saturated.
The hydrologic transport of radionuclides vertically by
trench water from the trench bottom to the aquifer and then
horizontally through the aquifer is modeled as one-
dimensional flow with a correction made for dispersion.
Because many of the submodels in the PRESTO-EPA-POP code
were initially developed for other types of assessments and
have been adapted to estimate health effects from shallow
land disposal of LLW, the code is modular in design to allow
submodels or subroutines to be replaced when desired or
necessary.
Annual hydrologic, climatic, and meteorologic data which are
used for a site can be based on the annual variations
recorded in 30-year or other long-term averages from a
nearby weather station and normalized for input into the
PRESTO-EPA-POP code.
« There are no significant changes assumed in farming practices,
demographics, water and foodstuffs usage, or climate during
the period of analysis.
The PRESTO-EPA-POP code uses unit response, bookkeeping, and scheduled
event types of submodels. The unit response submodels calculate the annual
response for a process. For example, the INFIL unit response submodel
calculates the annual infiltration through an intact trench cap. This
annual infiltration is then apportioned within each year by the bookkeeping
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submodels. Other unit response models calculate the atmospheric
radionuclide concentration transported downwind per unit source strength
and the annual average erosion of the trench cap.
Bookkeeping submodels follow the results of unit response submodels
and user-supplied control options. For example, the TRENCH submodel, which
maintains a water balance in the trench, calculates the maximum level of
standing water in the trench and the water volume annually leaving via the
trench bottom or overflow. Scheduled event submodels consider the events
such as cap failure, basement construction, the failure of container
integrity, and initiation of scheduled mechanical suspension of dust. The
timing for these events is specified by the user.
The Environmental Protection Agency wishes to warn potential users
that, like any complex computer code, the PRESTO-EPA codes can be misused.
Misuse could consist of using the code to examine a site where one or more
critical modeling assumptions are invalid, or where values for significant
input parameters are chosen that do not accurately reflect variables such
as radionuclide inventory, site meteorology, surface and subsurface
hydrology and geology, and future population demographics. Certain release
and transport scenarios, such as major changes in meteorology or mining of
the trench contents, are not considered in the PRESTO-EPA-POP model and
code. Significant changes to the existing code and the input data would be
required to consider such scenarios. The PRESTO-EPA codes were developed
to assess and compare alternative methods for managing and disposing of
LLW at generic sites for general scenarios. The codes were not developed
to analyze specific sites.
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1. INTRODUCTION
The U.S. Environmental Protection Agency (EPA) is developing a generally
applicable environmental standard for the disposal of low-level radioactive
waste (LLW) to support the U.S. Nuclear Regulatory Commission (NRC), the
U.S. Department of Energy (DOE) and others in developing a national radio-
active waste management system. As an aid in developing the standard, a
family of computer codes entitled PRESTO-EPA-POP, PRESTO-EPA-DEEP,
PRESTO-EPA-CPG, PRESTO-EPA-BRC and PATHRAE-EPA was developed under EPA
direction. The EPA uses the PRESTO-EPA code family to estimate and compare
the potential health impacts of a broad number of LLW disposal alternatives
for evaluation and support of the LLW standard. Table 1-1 provides a brief
description of each of these EPA codes. These codes, and how the EPA uses
them, have been described in detail (Gal84). Information on obtaining
complete documentation and users' manuals for the PRESTO-EPA family of
codes (EPA85a through EPA85i, MeySl, Mey84) is available from the EPA.
The PRESTO-EPA-POP code (Prediction of Radiation Effects from Shallow
Trench Operations - EPA - Population), which is the first member of the
family of PRESTO-EPA codes and the subject of this document, is designed to
permit the EPA to compare the relative potential population health effects
of different management and shallow land disposal alternatives for
low-level radioactive waste.
1.1 DESCRIPTION OF A LOW-LEVEL WASTE DISPOSAL SITE
The description of the life cycle of a shallow land disposal site is
useful in explaining the modeling approach. Following site selection and
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TABLE 1-1
PRESTO-EPA CODE FAMILY
PRESTO-EPA CODE
Purpose
PRESTO-EPA-POP
PRESTO-EPA-DEEP
PRESTO-EPA-CPG
PRESTO-EPA-BRC
PATHRAE-EPA
Estimates cumulative population health effects to local
and regional basin populations from land disposal of LLW
by shallow methods; long-term analyses are modeled
(generally 10,000 years).
Estimates cumulative population health effects to local
and regional basin populations from land disposal of LLW
by deep methods.
Estimates maximum annual whole-body dose to a critical
population group from land disposal of LLW by shallow or
deep methods; dose in maximum year is determined
Estimates cumulative population health effects to local
and regional basin populations from less restrictive
disposal of BRC wastes by sanitary landfill and
incineration methods.
Estimates annual whole-body doses to a critical
population group from less restrictive disposal of BRC
wastes by sanitary landfill and incineration methods.
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procurement, trenches are dug on the site. Waste materials in various
types of containers ranging from plastic bags or cardboard boxes to steel
drums are added to each trench. There is currently no standardized
container for LLW disposal. Once a trench is filled, or at various stages
of filling, the trench may be backfilled to eliminate voids and decrease
the potential for subsidence and cracking of the trench cap. Following
backfilling, the trench is covered with a cap of soil or clay, one to
several meters thick, mounded above grade to facilitate runoff of
precipitation and decrease infiltration. To minimize erosion in non-arid
climates, the cap is seeded with grass or cover crop and is maintained for
a number of years. Although not all burial operations are identical, most
current and past LLW facilities have included some of the practices
described.
In general, hydrologic transport is the major process by which the
general public may become exposed to radioactivity from LLW disposed in
shallow trenches. Figure 1-1 is a schematic description of the routes that
water, and any transported radionuclides, may follow from a trench in a LLW
disposal site. The major source of water at existing sites and, it is
anticipated, at future sites is precipitation. Precipitation at a site may
infiltrate the soil or trench cap, run off the surface, or evaporate.
Depending on the groundcover, length and steepness of slopes, and other
factors, runoff may cause erosion of soil from the surface.
Hydrologic transport of radionuclides from a LLW burial trench may be
by the groundwater or via the runoff. Groundwater or precipitation
entering the trench may mix with the waste material and become contaminated.
This contaminated water may either overflow the top of the trench or
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PRECIPITATION
ATMOSPHERIC TRANSPORT
RESUSPENSION
I ,
DEPOSITION
DRINKING WATER
ft IRRIGATION
TRENCH CONTAINING
LOW-LEVEL WASTE
TRANSPORT TO AQUIFER
AT RETARDED VELOCITIES
STREAM
WELL
AQUIFER
TRANSPORT THROUGH AQUIFER AT RETARDED VELOCITIES
FIGURE 1-1. ENVIRONMENTAL TRANSPORT PATHWAYS USED IN
PRESTO-EPA-POP.
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percolate downward through the bottom of the trench to the subtrench soil
zone and ultimately enter an aquifer. In most cases, particularly in the
arid southwestern United States, the disposal formation and much of the
geologic formations overlying the aquifer are only partially saturated.
Transport velocities are different for saturated and partially saturated
flow but can be calculated. The water in the aquifer will have a
characteristic flow velocity from a few meters per year to hundreds of
meters per year. Radionuclides that finally reach the aquifer generally
will be transported at velocities much lower than the characteristic flow
velocity of the water in the aquifer. This "retardation" is due to
interaction of the radionuclides .with the solid materials in the aquifer.
Some of the radionuclides in the aquifer may eventually reach the water
supplying irrigation or drinking wells or a point where the aquifer
communicates with surface streams. Water infiltration from the aquifer is
used by the local population. Residual radionuclides in the aquifer which
are not consumed by the local population are assumed to undergo further
transport to a large downgradient population (referred to as the "regional
basin" population). Health effects to the regional basin population are
calculated for a time period of up to 10,000 years.
A trench dug in material of low permeability may eventually overflow
if rainfall is high enough and if water infiltrating into the trench is not
removed. Once overflow has occurred, the radionuclides may be transported
by runoff to nearby streams and become available for human consumption via
irrigation or drinking, or else released to the regional basin through a
basin stream.
Humans away from the burial site may be exposed to the contaminated
water if this water is used for irrigation of food crops or drinking.
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Humans may also be exposed to radionuclides transported from LLW sites by
atmospheric processes. Radionuclides deposited on the soil surface by
trench overflow, by spillage during disposal operations, or by complete
erosion of the trench cap, may be suspended in the atmosphere and
transported downwind where they may be inhaled or deposited on the ground
and vegetation. Deposited radioactivity may contaminate crops, meat, and
milk and enter the food chain. Deposition on the soil surface may also
result in external radioactive exposure to humans.
Besides the transport pathways represented in Figure 1-1, there are
several other methods by which humans can be exposed to radioactivity from
a LLW disposal site. If the trench cap is eroded away, the wastes will be
more accessible to environmental transport processes. After the end of
institutional control of the site, an intruder could reside on or farm the
site. It is likely the intruder would receive an external exposure from
the buried radionuclides if excavation occurred near the trench. Factors
such as the length of residency, length of time after burial, and initial
radionuclide inventory would all contribute to the amount of exposure and
subsequent dose and health effects.
Farming the site may also result in off-site exposures to radioactivity
by mechanically suspending contaminated soil in the atmosphere. In contrast
to an off-site population, however, a farmer may ingest crops grown over
the trench where the nuclide uptake by roots will be higher, because nuclide
concentrations in the soil will be higher. Also, depending on when farming
started, the on-site irrigation water may contain higher concentrations of
radioactivity than off-site water.
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1.2 DESCRIPTION OF MODEL
The model has been designed to calculate the doses and health effects,
resulting from the disposal of low-level radioactive wastes, to a local
population and to the population in a hypothetical regional basin in which
the disposal site is located. The impacts on the local and regional basin
populations are analyzed for a period of up to 1,000 years. The regional
basin analysis can be extended at the option of the user for an additional
9,000 years, with the local population assumed to become part of the
regional basin population.
Many of the submodels included in PRESTO-EPA-POP were developed for
other types of assessments and have been adapted for the estimation of the
environmental transport of radioactive waste and ensuing health effects
from LLW disposal. Because of this, PRESTO-EPA-POP is modular in construc-
tion to allow for different versions of the submodels or subroutines to be
substituted, if desired.
PRESTO-EPA-POP first simulates the environmental transport of
radionuclides from the low-level waste trench to the environments of the
local and regional basin populations. Then the code calculates doses and
health effects using the DARTAB model for the local population, and a
separate health effects accounting model for the regional basin population.
The calculations in DARTAB are based on average internal intakes and
average external exposures. Internal intakes are due to ingestion of
contaminated foods and water, and inhalation of contaminated air. External
exposures are due to contaminated air and contaminated soil. For a
detailed account of the DARTAB methodology, see Section 2.3 of the DARTAB
documentation report (Be81).
1-7
-------
The health effects calculations for the regional basin population are
based on the cumulative amount of radionuclides released to the regional
basin through a basin stream during the assessment period for the regional
basin, which is usually 10,000 years. The transport portion of the
regional basin submodel provides the cumulative amount of radionuclides
discharged into the downstream basin. The subsequent health effects are
calculated by using precalculated healtheffect conversion factors for each
radionuclide and region.
The population health effect assessment begins immediately after the
closure of the disposal site. The radionucl ide inventories of the wastes
in the trench are calculated to account for the radioactive decay during
the operational period. The waste is assumed to be containerized so that
the leaching of radionuclides from the waste cannot begin until the
container fails. The length of the container integrity is a user specified
parameter; therefore, a zero time should be specified when the waste is not
physically containerized or no credit is given for container integrity.
The code was developed to handle a wide variety of hydrogeologic and
climatic situations. It can also handle waste leaching and the groundwater
transport of nuclides under partially saturated as well as saturated hydro-
geologic conditions, while taking into account nuclide retardation due to
hydrogeochemical processes. The code has features to account for the decay
of the leaching process resulting from the use of waste containers; a
farming scenario which simulates farming over the trench with vegetation
root uptake of radionucl ides from the waste; and reduction in the trench
radionuclide inventory at the start of simulation because of decay during
the operational period.
1-8
-------
The ingrowth of radioactive decay products is not calculated by the
model to maintain simplicity and to reduce computer time and expense. In
cases where the major dose contribution is from external exposure to a
short-lived progeny in equilibrium with a parent radionuclide present in
the trench inventory, the user may wish to include the progeny in the
trench inventory by a method described at the end of Section 2.2.3.
Operational spillage is defined as radionucl ides spilled from incoming
waste packages and remaining on the ground surface at the close of disposal
operations. These radionuclides would subsequently be transported either
by the atmospheric pathway to the local population or by the surface water
pathway to the nearby stream.
The complex physical and chemical interaction between the radionuclides
and the solid geologic media has been grouped into a single factor, the
distribution coefficient, viz., Kd. Different Kd values can be used for
soil, the mixture of soil and waste material in the trench, sub-trench
soil, and the aquifer.
The subsurface transport path of radionuclides is assumed to be
vertical from the trench bottom to the aquifer and then horizontal through
the aquifer. The flow in the vertical strata can be calculated either as
saturated or unsaturated flow, depending on the relationship between the
rate of exfiltration, the degree of saturation, and the properties of the
geologic media. However, flow in the aquifer is assumed to be saturated.
The transport of radionuclides in the aquifer is calculated by employing
Hung's "optimum groundwater transport model" (Hu81). The model also uses
Hung's correction factor which was designed to compensate for the dilution
effects of dispersion on the health effects evaluation.
1-9
-------
Three types of submodels are used in the PRESTO-EPA-POP code: unit
response submodels, bookkeeping submodels, and scheduled event submodels.
The unit response submodels calculate the annual response of a give process.
For example, the submodel INFIL calculates the annual infiltration through
an intact trench cap. This annual infiltration is then apportioned among
the transport processes by the bookkeeping submodels. Other unit response
models calculate the annual average atmospheric dispersion coefficient and
erosion from the trench cap.
Bookkeeping submodels keep track of the results of unit response
submodels and user-supplied control options. For example, the TRENCH
submodel maintains a water balance in the trench, calculates the level of
standing water in the trench, and the volume of water leaving the trench.
Average concentrations of each radionuclide over the assessment period
in environmental media, such as well water or the atmosphere, are used to
calculate radionuclide concentrations in foodstuffs. Foodstuff
concentrations and average human ingestion and breathing rates are utilized
to calculate the annual average radionuclide intake per individual in the
local population by ingestion and inhalation. These intake data are then
used to estimate dose rate and health effects.
The atmospheric transport calculations made by the code assume that
the total population resides within the same 22.5-degree sector.
User-specified parameters give the fraction of year that the plume blows in
that sector. Therefore, each member of the population, breathing at the
same rate, will inhale the same quantity of each radionuclide. An external
code, RADE (EPA85i), allows the user to replace the atmospheric dispersion
calculation made for a 22.5 degree sector by the PRESTO-EPA-POP code with
1-10
-------
an externally calculated equivalent dispersion coefficient for a number of
Population centers in a 360 degree circle enclosing the disposal site. The
RADE computer code is briefly described in Appendix C.
Each person in the local population is assumed to eat the same
quantities and varieties of food, all grown on the same fields, and obtains
his or her drinking and crop irrigation water from the same source. This
assumption simplifies the calculations and is appropriate because of the
large uncertainties in predicting individual mobility, population demo-
graphy, agricultural practices, geologic and hydrologic changes that might
occur during the 1,000 year local analysis period. As input parameters,
the user may specify the fraction of the drinking and irrigation water that
is supplied by the contaminated well or stream.
Doses and health effects to populations are calculated by
characterizing the population center for each site with a single geographic
centroid location and the total population. In calculating the health
effects, the population age distribution and size is held constant over the
assessment period.
Scenarios resulting in radiological exposure from the buried waste may
be modified by changing input parameters. These scenarios include: normal
disposal site operations; spillage of wastes during disposal operations; a
resident intruder on the site; farming of the site; and an eroded trench
cap with subsequent atmospheric contamination via suspension of mixed waste
material and soil. By changing the site description parameters, the user
may design other scenarios of interest. To satisfy the needs of EPA for an
assessment of the total impact of a disposal facility, the code is designed
to make calculations for combinations of all reasonable exposure pathways
1-11
-------
for a given scenario. The exposure pathways for each of four scenarios are
listed in Table 1-2.
Additional assumptions in the model and features of the code follow:
Annual average meteorology for the site is part of the
required input data.
All members of the population use the same sources of
drinking and irrigation water contaminated from trench
seepage or overflow.
The population age distribution and size are held constant
over the assessment period.
The user can specify the fraction of the drinking and
irrigation water that is supplied by the contaminated well
or stream.
Doses and health effects to populations are calculated from
population centers for each site characterized by a single
geographic centroid location containing the total
population.
Exposure from the eroded trench occurs when the trench cap
has become completely removed by either erosion or mechanical
means. Thereafter, the eroded trench scenario may provide
for suspension and atmospheric transport of trench contents
and resulting inhalation by an individual or the specified
population.
An individual may be directly exposed to trench contents and
thus receive an external dose. The population may receive
an external dose from immersion in the suspended plume.
The code is structured to consider only one scenario per
computer run. The scenario to be simulated may be designed
by the input values a user chooses for such parameters as
population size, location and distance to well, percent cap
failure, resuspension rate, etc.
1.3 OUTLINE OF METHODOLOGY MANUAL
Chapter 1 provides an introduction to and basis for the PRESTO-EPA-POP
code. The description is given of a shallow land disposal site for LLW and
the potential pathways by which radiation exposures to humans might occur.
1-12
-------
TABLE 1-2
RADIOLOGICAL EXPOSURE PATHWAYS FOR SELECTED SCENARIOS
Scenario
Normal
Farming
Eroded Trench
Local Population
Ingests off-site water
Ingests off-site foods
Inhales downwind air
Ingests on-site foods
Ingests off-site water
Inhales suspended material
at geographic centroid
Direct exposure from plume
1-13
-------
In Chapter 2 a detailed discussion is found of the methodology
employed in developing the quantitative models for evaluating environmental
transport pathways and calculating the radiation doses, associated risks
and potential health effects to individuals and selected populations.
Appendices A and B provide background information in support of the models
employed in the code.
Chapter 3 provides a description of the structure of the PRESTO-EPA-POP
code and its subroutines.
Chapter 4 provides a detailed description of the output data as
produced by the PRESTO-EPA-POP code.
The PRESTO-EPA-POP Users Manual (EPA85b) provides detailed information
and guidance in the use of the code together-with sample problems and a
source listing of the code.
1-14
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2. DISCUSSION OF METHODOLOGY
2.1 ENVIRONMENTAL TRANSPORT PATHWAYS
Pathways for environmental transport of radionuclides considered by
the model are shown in Figures 2-1 and 2-2. Pathways of environmental
transport of radionuclides that involve water (Figure 2-1) include both
surface water and groundwater. Water may leave the trench through the
bottom or by overflowing. The user may also choose to allow the soil
surface to be contaminated initially by operational spillage. Radionuclides
in water near the soil surface may be transported to a surface water body
or may enter the aquifer by deep seepage. Contaminated water may ultimately
reach the local population by use of water from either a well or surface
water. The regional basin population will be exposed to the radionuclides
that enter the regional basin stream from the surface water body and
groundwater. Surface water transport to the basin use point is assumed to
take less than one year, while the groundwater transport takes a much
longer time, depending on the distance of travel from the local to the
basin use points and the distribution coefficient of the radionuclide.
Radionucl ides not used by the regional basin population are assumed to
enter the ocean which acts as a radionuclide sink.
Atmospheric pathways for radionuclide transport considered by the
model are illustrated in Figure 2-2. Material may reach the atmosphere
from the site soil surface contaminated by overflow or operational
spillage, or by the denuded trench following possible erosion of the total
cap sometime in the future. The local population may ultimately be
impacted by inhalation of or immersion in the suspended materials downwind,
2-1
-------
SPILLAGE
1
s
OVERFLOW
f i
f
SOIL
>URFACE
LEAC
HING
TRENCH
LEAC
^
HING
\
VERTICAL
SOIL
COLUMN
BASIN
POPULATION
OCEAN
SINK
SEEPAGE
GROUNDWATER TRANSPORT
DRINKING INGESTION DRINKING
\
HUMANS
RAE-102206
FIGURE 2-1. HYDROLOGIC ENVIRONMENTAL TRANSPORT PATHWAYS
2-2
-------
SURFACE
CONTAMINATION
ERODED
TRENCH
SUSPENSION
LL
AIR
INHALATION
IMMERSION
HUMANS
(Local Population)
DEPOSITION
IRRADIATION FROM GROUND
INGESTION
CROPS
AND
GROUND
RAE-102094
FIGURE 2-2. ATMOSPHERIC ENVIRONMENTAL TRANSPORT PATHWAYS.
2-3
-------
by ingestion of crops contaminated following deposition on soil or crops,
or by direct irradiation from ground surfaces. The impact of the
atmospheric pathway on the regional basin population is considered to be
negligible because of its distance from the disposal site and, therefore,
no calculations are made for the atmospheric pathway.
The approach of the PRESTO-EPA-POP code to calculating radionuclide
concentrations in the pertinent environmental media is described in the
following two sections.
2.1.1 Transport Pathways Involving Water
At many sites, water is the most important medium for transport of
radionuclides away from the trench. Whether the transport pathway is
predominantly by groundwater or by overland flow of water, an important
quantity is the amount of water entering the trench via infiltration
through the trench cap.
The basic model for simulating the annual infiltration of
precipitation assumes that it occurs in two modes: (1) annual average
infiltration which is dependent upon the inherent physical properties of
the trench cap and (2) infiltration through failed portions of the trench
cap. Annual average infiltration depends upon soil properties, seasonal
and annual temperatures, amounts of precipitation, rates of evapotranspira-
tion, and other similar physical parameters. Infiltration through failed
portions of the trench cap increases with time from zero at the beginning
as the percent of trench cap failure increases. The year when failure
begins, the rate of failure, and the final percent of failure are specified
by the user and determine the amount of infiltration due to cap failure.
2-4
-------
Infiltration Through Trench Cap - The basic model for simulating the
annual infiltration through the trench cap assumes a portion of the trench
cap will fail and allow the precipitated water to drain into the trench.
The fraction of the trench which fails is assumed to vary with time.
Due to the distinct nature of the infiltration mechanism between the
intact portion and the failed portion of the trench cap, the annual
infiltration through the trench cap is divided into separate components.
On the intact portions of the cap, the normal infiltration rate is
calculated by the method developed by Hung (Hu83b) which is described in
Appendix A. For the failed portion of the cap, the infiltration is the sum
of rainfall plus irrigation. Therefore, the volume of water entering the
trench annually is calculated by
WT = AT[fc(Pa+Ia)+(l-fc)WaJ (2-1)
where
Wj = volume of water entering trench in current year
Ay = area of trench (m^)
fc = fraction of trench cap that has failed (unitless)
Pa = annual precipitation (m)
Ia = annual irrigation (m)
Wa = annual infiltration (m)
The value of Wj is added to the standing trench water from the earlier
year to calculate the maximum depth of standing water in the trench for the
current year.
2-5
-------
The component of annual infiltration through the intact portion of the
trench cap, Wa, is estimated by employing the infiltration model developed
by Hung (Hu83b, Appendix A). The model simulates the rate of infiltration
by solving system equations which describe the dynamics of overland flow,
subsurface flow, and atmospheric dispersion systems. The basic equations
employed in the model are
Qo = liH^iH5/3 (2.2)
(2-3)
EO =
En when P + > En
p At p
P + ?- when ED > P + > 0
At P At
u
0 when P + =0
At
Ks when P - E0 + > K<-
At s
P - E0 + - when Kc > P - En + > 0
At b ° At
0 when P - En + £- = 0
0 At
max
Ks when Zg < Z,
0 when Zg = Zmax
dt
= (qi - q0 + qt)/wg
(2-4)
(2-5)
(2-6)
(2-7)
(2-8)
2-6
-------
'F - F '
.tp to*
1 +
0.66(Wp
-1
2-9
dZp/dt = -fqp + qt)/Wp (2-10)
qt = ) qo when Zp > 0 (2_n)
0 when Zp = 0
and qp = -Max( qL , qv ) (2-12)
where
Q0 = rate of overland flow per unit width of trench cover (m^/m-hr)
H = average depth of overland flow over the entire trench cover (m)
L = length of slope or half of trench width (m)
n = Manning's coefficient of roughness
a = average inclination of the trench cover (m/m)
P = rate of precipitation (m/hr)
EQ = rate of evaporation from the overland flow (m/hr)
q0 = rate of percolation from the overland flow system (m/hr)
Ep = evaporation potential (m/hr)
q-j = flux of moisture infiltrating into the trench (m/hr)
q^ = flux of pellicular water transported in the liquid phase (m/hr)
Ks = saturated hydraulic conductivity of the soil (m/hr)
Zq = deficit of gravity water (m)
Zmax = maximum deficit of gravity water, equivalent to the thickness
of the trench cover (m)
Wq = component of wetness for the gravity water under a fully
saturated condition, numerically identical to the porosity
for the gravity water (unitless)
qL = flux of pellicular water transported in the liquid phase (m/hr)
2-7
-------
Wp = component of wetness for the pellicular water under fully
saturated condition and is numerically identical to the
porosity for pellicular water (unitless)
Zp = deficit of the pellicular water (m)
De = hydraulic diffusivity at equivalent wetness (m2/hr)
Ke = hydraulic conductivity at equivalent wetness (m/hr)
qv = flux of moisture being transported in the vapor phase (m/hr)
qt = flux of moisture being transformed from gravity water to
pellicular water (m/hr)
qp = flux of pellicular water (m/hr)
The annual infiltration through the trench cap is then calculated by
integrating the hourly infiltration over the entire year.
Trench Cap Modifications - The trench cap may fail by erosion or
mechanical disturbance. In the case of erosion, the annual thickness of
material removed from the trench cap by sheet erosion is calculated using
an adaption of the universal soil loss equation (USLE) (Wi65).
The annual amount of erosion is subtracted from the cap thickness for
the current year of simulation. If the remaining thickness is less than
1 cm, the cap is considered to be completely failed and fc is set to 1.0.
The USLE may be written as
1L = fRfKf!_fSfcfpfD (2-13)
where
IL = yearly sediment loss from surface erosion (tons/ha)
fR = rainfall factor (fR unit or 10Q m-tons-cm/ha)
f|< = soil credibility factor (tons/ha/fR-unit)
f[_ = slope-length factor (unitless)
2-8
-------
fs - slope-steepness factor (unitless)
fc = cover factor (um'tless)
fp = erosion control practice factor (unitless)
fD = sediment delivery factor (unitless)
The parameterization scheme of McEl roy et al. (McE76) was used to
specify site-specific values of the factors in Equation (2-13). The
rainfall factor, fR, expresses the erosion potential of average annual
rainfall in the locality. The soil credibility factor, fK; is also
tabulated by McEl roy et al. as a function of five soil characteristics:
percent silt plus very fine sand; percent sand greater than 0.1 mm; organic
matter content; soil structure; and permeability. The factors, f|_ and f$,
for slope-length and steepness account for the fact that soil loss is
affected by both length and degree of slope. The PRESTO-EPA-POP code usage
of USLE combines both factors into a single factor that may be evaluated
using charts in McElroy et al. The factor, fc, represents the ratio of the
amounts of soil eroded from land that is treated under a specified
condition to that eroded from clean-tilled fallow ground under the same
slope and rainfall conditions. The erosion control practice factor, fp,
allows for reduced erosion potential by the effect of practices that alter
drainage patterns and lower runoff rate and intensity. The sediment
delivery ratio, fn., is defined by McElroy et al. as the fraction of the
gross erosion that is delivered to a stream.. Units of I|_ are converted to
(m/yr) within the code. See Chapter 4 for a description of input units.
The second method of trench cap failure accounts for the possibility
of mechanical disturbance due to human intrusion or some other means which
might completely destroy portions of the cap. This phenomenon can be
termed a partial failure, but in reality is a total failure of some part of
2-9
-------
the cap. The code user may specify some rate of cap failure as shown in
Figure 2-3. By specifying appropriate values for the (x,y) pairs in
Figure 2-3, the user may selectively remove the cap from a portion of the
trench area. Mathematically this function is represented by
0 if tNYR2
Even though PCT2 might be less than 1.0 in year NYR2, the cap may
ultimately fail completely by virtue of erosion. As f^ changes, the amount
of water added to the trench annually also changes.
The amount of water leaving the trench annually via the trench bottom
is calculated by
(DW+L)ITAT
VB = W L T T (2-15)
and
DW = VATWT (2-16)
where
Vg = volume of water leaving trench bottom annually (
D\fj = depth of water in trench during current year (m)
Ij = permeability of material below the trench (m/yr)
Aj = trench area (m2)
V^j = volume of water in trench (m^)
WT = porosity of trench contents (unitless)
L = length of saturated zone (m)
2-10
-------
<|3
£°
Li. ^
Ojf
zee
Q>
o
o
ro
PCT1
o
i
NYR1 NYR2
TIME (Years)
RAE-102^24
FIGURE 2-3. TRENCH CAP REMOVAL FUNCTION.
2-11
-------
Water will overflow the trench if the maximum depth of standing water
is greater than the trench depth. If this is the case, the overflow is
calculated by
V0 = (DW-DT)ATWT (2-17)
where
VQ = volume of water overflowing trench in a year
D^ = depth of water in trench (m)
Dj = trench depth (m)
Aj = trench area (m2)
Wj = porosity of trench material (unitless)
Water in the trench may be contaminated by contact with the waste
material. The user must choose one of five methods shown in Table 2-1 to
calculate the concentration of radionucl ides in the trench water.
Options 1-4 are combinations of two factors: the amount of waste
material contacted by water and the method of partitioning contamination
between waste and water. In options 1 and 3, where the waste is in total
contact with the trench water, it is assumed that the total volume of
wastes in the trench is wetted each year as water trickles from top to
bottom in the trench. In options 2 and 4, wherein the wastes are not
totally immersed in trench water during the entire year, the submodel
(immersed fraction) calculates the wetted fraction as the ratio of maximum
water depth to trench depth. Leaching options, 1 and 2, utilize a
distribution coefficient, Kd, to estimate the radionuclide concentration cj
in the trench water based on chemical exchange (Equation 2-18a)
2-12
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TABLE 2-1
LEACHING OPTIONS SPECIFIED BY LEAOPT
Option Leach Calculation Method
1 Total contact, distribution coefficient
2 Immersed fraction, distribution coefficient
3 Total contact, solubility
4 Immersed fraction, solubility
5 Release fraction
2-13
-------
TCON
(Chemical Exchange Option) (2-18a)
,T
= Mi n
SNCNV ITfw
(Solubility Option) (2-18b;
DmaxATwT
and
TCON = Min [TINFL/PERMT, 1]
where
TCON = estimates the average annual fraction of the time that the
waste is in contact with the trench water
TINFL = annual infiltration rate (m/y.r)
PERMT = trench hydraulic conductivity (m/yr)
Cy = concentration of radionuclide in trench water (Ci/cm^)
Iy = amount of nuclide in trench (Ci)
f|d = fraction of total waste contacted by water (=1 for LEAOPT = 1;
<1 for LEAOPT = 2)
Ay = trench area (m^)
Dmax = maximum depth of standing water (m)
Wj = porosity within trench (unitless)
DT = trench depth (m)
K,j2 = distribution coefficient within waste for radionuclide (ml/g)
Pw = density of waste material (g/cm^)
S = elemental solubility (g/ml)
M = mass of radionuclide (g/mole)
Nc = ratio (Ci/mole)
Nv = ratio (ml/m^)
2-14
-------
Leaching options 3 and 4 use a solubility factor to estimate the
maximum concentrations of radionuclides in the trench water. The
solubility option may be used when information concerning K
-------
transport is retarded, relative to the movement of water, by vertical and
horizontal retardation factors, RV and RH> as explained below:
The groundwater flow in the vertical reach is assumed to be saturated
or partially saturated. The degree of saturation is used to calculate the
water velocity, Vv and the vertical retardation factor, Ry. The degree of
saturation, SSAT, is either read in as an input parameter, or is calculated
from the equation
SSAT = RESAT + (1-RESAT) /AJJ[NEk\0-25 (2-19a)
\ PERMV /
where
RESAT = residual moisture content, expressed in a fraction of total
water content when saturated (unitless)
ATINFL = average exfiltration rate (m/yr)
PERMV = vertical saturated hydraulic conductivity (m/yr)
Equation (2-19a) is based on approximate expressions for the fraction
of saturation (Cla78, McW79). The exponent, 0.25, is generally a function
of soil type, but has been assigned a conservative fixed value for
simplicity. The residual moisture content, RESAT, is an input parameter
that is generally identical to the input parameter Wp of the INFIL submodel.
The parameter ATINFL is the average trench exfiltration rate. When there
is no overflow of trench water, the rate is calculated by the expression
ATINFL = [PCT2 (PPN+XIRR)+(2-PCT2) XINFL]0.5 (2-19b)
where
PCT2 = maximum fraction of trench cap failure (unitless)
PPN = annual precipitation rate (m/yr)
2-16
-------
XIRR = annual irrigation rate (m/yr)
XINFL = infiltration rate through the intact trench cap (m/yr)
(calculated by the INFIL subroutine)
Vertical water velocity Vv (m/yr), and the vertical retardation factor
Rv (unitless) are calculated as follows:
Vv = ATINFL/(PORV-SSAT) (2-19c)
Rv = 1 + (BDENS-XKD3)/(PORV-SSAT) (2-19d)
where
BDENS = host formation bulk density (g/cm^)
XKD3 = distribution coefficients for the host formation (ml/g)
PORV = subsurface porosity (unitless)
On the other hand, the horizontal retardation factor, R^, is calculated as
RH = 1 + (BDENS-XKD4)/PORA (2-19e)
where
XKD4 = distribution coefficient of the aquifer (ml/g)
PORA = aquifer porosity (unitless)
Finally, the vertical horizontal transit time, ty (yr), and t^ (yr),
are calculated according to
tv = L , tH = l (2-20)
VH
where
DV = distance from trench to aquifer (m)
DH = length of aquifer flow from trench to well (m)
2-17
-------
Vy = vertical water velocity (m/yr)
VH = water velocity in aquifer (m/yr)
Retardation, RV and RH, are as previously defined.
The breakthrough time, which "is the time required for a radionuclide
to travel from the bottom of the trench to the well, is the sum of the
vertical and horizontal transit times. A second horizontal transit time is
also calculated by the model, which is the time it takes for a radionuclide
to migrate in the aquifer from the well point to the point of release to
the basin stream. This transit time is calculated using the corresponding
horizontal distance from the well to the basin stream.
The transport of radionuclides in the aquifer is evaluated by
employing Hung's groundwater transport model (Hu81, Hu86, Appendix B). The
basic equations for the model as adopted from Hung are
Q = zQ0 (T-RL/V) Exp(-Xt) (2-21)
oo
and z = /0.5(RP/7rW3)1/2 Exp C-NdW-(PW/4R)(R/W-l)2] dW (2_22
° Exp(-RNd)
Exp - P-
2 2 f PV J
c /
Exp (
where
z = a correction factor to compensate for the dispersion effect
R = retardation factor, RV or RH
2-18
-------
P = Peclet number, VyDy/d or
W = dimensionless time, yV/L
Nj = decay number, XL/V
L = flow length, Dy or DH (m)
V = water flow velocity, Vy or V^ (m/yr)
t = transit time, ty or t^ (yr)
d = dispersion coefficient (m^/yr)
= radiological decay constant (yr~l)
y = dummy time variable (yr)
Q = rate of radionuclide transport at distance L from the source
(Ci/yr)
Q0 = rate of radionuclide released at the source (Ci/yr)
T = time of simulation (yr)
To calculate the radionuclide concentration at the well point, the
rate of groundwater flow in the plume of contamination at the well point is
calculated by
WA = VAPADA[V^T~+ 2 " tan(a/2)DH] (2-23a)
where
WA = the rate of contaminated water available for removal from well
(m3/yr)
VA = groundwater velocity (m/yr)
PA = porosity of aquifer material (unitless)
DA = thickness of the aquifer (m)
a = constant angle of spread of the contaminant plume in the
aquifer (radians)
Ay = trench area (m2)
D = trench to well distance (m)
2-19
-------
The angle "a" is the dispersion angle of a contaminated plume in the
water in an aquifer. This dispersion angle may be empirically determined
(e.g., by field dispersion tests wherein the angle of dispersion is
determined from measurements of chemical, conductivity, or radioactivity
tracers in water from a series of boreholes downstream across the plume) or
it may be estimated. The use of a dispersion angle is consistent with
published characterizations of the horizontally projected profile of a
chemical contamination front as it moves through an aquifer (Sy81).
The radionuclide concentration in the well water, Cy (Ci/m3), is
calculated by
CW = -2- (2-23b)
wA
The total water demand, Vy, including drinking water, cattle feed, and
crop irrigation, is calculated by
Vu = [3.9X107WIfILI+UwLH+1.5X104LA]Np (2-24)
where
Vu = annual well water demand in liters (1/person yr)
3.9X107 = 4492 m2 irrigated per person X 8760 hr/yr
Wj = irrigation rate per unit area (1/m2 hr)
fj; = fraction of year when irrigating (unitless)
UN = individual annual water consumption (1/person yr)
LH = fraction of drinking water obtained from well water
4
1.5x10 = water fed to cattle consumed by humans (I/person yr)
LA = fraction of cattle feed water obtained from well water
Np = size of the population (persons)
Lj = fraction of irrigation water obtained from well water
2-20
-------
If the calculated total water demand, Vy, exceeds the flow rate of the
contaminated plume, W/\, the concentration of radionucl ides in the pumped
out water is recalculated using the actual volume of pumping to correct for
the dilution effect from the non-contaminated groundwater. Units of Vy are
converted to cubic meters within the code.
The calculated concentrations of radionuclides in well water are
averaged over the length of the simulation and used by the food chain and
human exposure parts of the code for the drinking water and cattle feed
pathways.
Trench Overflow Transport and Stream Contamination - As previously
mentioned, water will overflow the trench onto the soil surface when the
maximum depth of standing water is greater than the trench depth. If this
occurs, radionuclides will be added to the surface inventory of radionuclides
deposited by initial operational spillage. The surface soil will then have
a component adsorbed by the soil with concentration C$ (Ci/kg) and a compo-
nent of contaminated water in the surface soil of C^ (Ci/m3). The material
adsorbed by the soil will remain in the soil and becomes a source term for
resuspension and atmospheric transport (this process is discussed in
Section 2.1.2). The contaminated water in the surface soil is available to
enter nearby surface water bodies via overland flow, or percolate down to
the aquifer.
Radionuclides dissolved in the soil water may either be transported to
the stream by overland flow or to the deep soil layers by percolation. The
amount of each radionuclide added to the stream is represented by the
product of C^ the radionuclide concentration in the surface soil water,
and the annual volume of runoff from the contaminated soil surface, WSTREM.
c
The value of GW for each radionuclide is calculated by
2-21
-------
(2-25)
KdlMS+MW2/Pa
where
CM = radionuclide concentration in surface soil water (Ci/m3)
IS = amount of radionuclide on surface (Ci)
Kdi = distribution coefficient for surface soil region (ml/g)
MS = mass of soil in contaminated region (kg)
Myj2 = mass of water in contaminated soil region (kg),
Pa = density of water (1 g/cm3)
103 = conversion factors used for Kd(l ml/g = 1 m3/103 kg) and for
dw (1 g/cm3 = 103 kg/m3).
Equation 2-25 is used to compute the concentration of radionucl ides in the
surface soil interstitial water.
The radionuclide concentration in the contaminated surface soil
region, C$, is calculated using
GS = 10-3CwKdl (2-26)
The contaminated region of surface soil is defined by the user in
terms of length, S|_ (m), width, Syj (m), and depth, SQ (m). These
parameters allow the calculation of soil mass (M$) and the water mass (M^)
in the contaminated soil region by
MS = 103PSSWSLSD, MW = 103WSSWSLSD (2-27)
where
PS = soil bulk density (g/cm3)
W$ = soil porosity (unitless)
103 = (cm3 kg/m3 g) for soil and (kg/m3) for water
2-22
-------
Water falling on the contaminated soil region may either evaporate,
run off, or infiltrate. Of the liquid, a certain fraction of the total
precipitation, fr, will enter the stream annually-
The amount of water that enters the stream from runoff of the contami-
nated region is given by
Ws = frPSwSL (2-28)
The amount of water that enters deep soil layers and eventually the aquifer
is given by
WD = WaSwSL (2-29)
where Wa is the yearly farmland infiltration parameter.
The annual contribution of radionuclides from the contaminated surface
soil region to the stream, R$, is then the product of Ws and the radio-
5
nuclide concentration in the surface soil water C^ (Equation 2-25). The
amount of each radionuclide annually entering the deep soil layers from the
contaminated surface soil region is the product of WD and C^. The concen-
tration of radionuclides in the stream is the quotient of R$ and the annual
flow rate of the stream.
As with water removal from the well, the amount of each radionuclide
removed from the stream is conserved by using
IP = [3.9 x 107 WjfjS! + UWSH + 1.5 x 104SA] Np C* (2-30)
where
IP = annual amount of nuclide removed from stream (Ci)
CR
= radionuclide concentration in stream (Ci/m3\
n
2-23
-------
Si - fraction of irrigation water obtained from stream
SH = fraction of drinking water obtained from stream
S/\ = fraction of cattle feed water obtained from stream
Other parameters are the same as defined in Equation (2-24).
If Ip is larger than the annual input of that nuclide to the stream, R$,
then the radionuclide concentration in the stream is recalculated referencing
the water volume removed from the stream rather than the stream flow by
R RS
Cu= (2-31)
w vy
Mean concentrations of each radionuclide in well water and stream
water are calculated for the appropriate number of simulation years by
dividing the sum of the annual radionuclide concentrations in the well
water and the stream water by the length of the simulation.
2.1.2 Atmospheric Transport Sources and Pathways
For some sites, atmospheric transport of radionuclides may be a major
transport mechanism. Therefore, careful consideration must be given in the
formulation of the atmospheric transport model. Another factor which was
considered in generating PRESTO-EPA-POP was the desire to minimize the
amount and complexity of input data. The compromise solution to these
conflicting considerations was to employ in the code a simplified, compact
algorithm suitable for those sites where the population is concentrated
into a single, small community, and to make provision in the input data set
to allow the code user to enter an externally computed population average
value for the air concentration, X, to source strength, Q, ratio. An
externally computed X/Q ratio should be used for complex population
2-24
-------
distributions. An example of a code which could be used for determining
X/Q in such cases is AIRDOS-EPA (Moo79).
In most cases, the uncertainties in the computed atmospheric source
strength for contaminated areas are larger than the differences between the
internally computed and externally determined (using a code such as
AIRDOS-EPA) X/Q ratios. Use of an external code has several advantages,
however, the most salient being that explicit specification of complex
population distributions and the site wind rose removes the possibility of
the code user making errors of judgement in determining population
centroids.
Internal Model Capability and Formulation - The atmospheric transport
portion of the PRESTO-EPA-POP code will be discussed in two parts: (a) a
description of source strength computation and (b) a discussion of the
calculation of atmospheric concentration at the residence site of the
specified at-risk population. For most applications, PRESTO-EPA-POP is
expected to be applied to a site of known population distribution, and the
user must input geographical and meteorological parameters characterizing
the population site and its relationship to the low-level waste disposal
area. The formulation of atmospheric transport discussed herein is not
intended to automatically identify regions of high risk; rather, it is
formulated to calculate risk-related parameters for a particular, identified
site.
Where population health effects are to be determined, the geometric
population centroid specified by the user is the point for which a
22.5-degree sector average ground level air concentration is determined.
Where the population distribution subtends from the waste disposal area an
2-25
-------
angle significantly greater than 22.5 degrees, the user should run the code
separately for each sub-population. A mean yearly value for the
sector-averaged atmospheric concentration is computed by PRESTO-EPA-POP and
is input to DARTAB for use in computing external exposures.
The most common approach used for estimating the atmospheric
concentration and deposition of material downwind from its point of release
is the Gaussian plume atmospheric transport model (S168). This approach is
versatile and well documented. We have chosen to implement a Gaussian
plume transport code called DWNWND (FiSOa) as a module, in subroutine form,
in the PRESTO-EPA-POP code.
User inputs for the atmospheric transport simulation allow specifica-
tion of a surface radionuclide concentration at the waste disposal site.
Parameters used here include the initial surface radionuclide inventory and
the chemical exchange coefficient for surface soils. The portion of
radionuclide sorbed onto soil particles is considered available for
transport. A source strength is computed based either on a time-dependent
(monotonically decreasing) resuspension factor or a process-dependent
mechanical suspension variable. The given LLW site is described by
meteorological variables including:
FN = fraction of the year wind blows toward at-risk individuals
H = source height (m)
H|_ = lid height (m)
S = stability class
T(j = type of dispersion formulation
Hr = Hosker roughness parameter (m) (about .01 of the actual
physical roughness)
u = wind velocity (m/s)
2-26
-------
V(j = deposition velocity (m/s)
Vg = gravitational fall velocity (m/s)
x = distance from source to receptor (m)
Source Term Characterization - The release rate for atmospheric
transport is termed the source strength. In PRESTO-EPA-POP, the source
strength is directly dependent on the surface soil-sorbed radionuclide
concentrations from operational spillage and trench overflow, CQ (Ci/m2).
The source strength is the arithmetic sum of two parts: that parameterized
by a time-dependent resuspension factor, Re, (An75) and that parameterized
by a resuspension rate, Rr, (He80).
First, the wind-driven suspension component is described. If the
time-dependent resuspension factor is defined as
Re = ReiexP(Re2yT)+Re3 (2-32)
where T is elapsed time (days) and Re has units of inverse meters, then the
atmospheric concentration above the site, C^, is given by
CA = ReCG (2-33)
and CG = CS PS SD 1()3 (2-33a)
Using Anspaugh's values of IxlO"4, -0.15, and IxlO"9 for Rei, Re2> and
Re3, respectively, the value of Re calculated as above is probably
conservative for humid sites. As additional data from humid sites become
available, model users may wish to update the equation used for computing
Re.
2-27
-------
The value of elapsed time appearing in Equation (2-32) is computed
from the start of the simulation. It is, therefore, correct for the
initial surface inventory, but not for incremental additions thereto, which
may occur at later times. However, when later additions result from trench
overflow, they will likely consist of dissolved material and would likely
act as surface depositions of mobile particul ates. It is, therefore,
assumed that a steady-state asymptotic value of Re is for most sites
appropriate for later additions to the surface inventory.
The user wishing to specify a time independent windblown resuspension
factor may do so by setting the values of Rei and Re2 to zero. When this
is done, determination of windblown suspension of all contributions to the
surface inventory will be treated identically, regardless of time of
occurrence.
In the above expression, C/\ is the atmospheric concentration of radio-
nuclide immediately above the site at a height of about 1 m (Shi76), for a
site of large upwind extent. Large upwind extent may be interpreted as
exceeding the atmospheric build-up length, given by u Hp/Vq, where u is
wind velocity in m/s, HQ is the mixing height (=1 m) , and Vg is the
gravitational fall velocity. The representative site extent used in the
PRESTO-EPA-POP code is the square root of the site area, A (which is
characterized by S|_S^), and a tentative correction fraction, F. The
correction factor is computed using the equation
(2-34)
uHD
With the stipulation that the value used' for F may not exceed unity,
the source term component (Ci/s) for windblown suspension is given by
2-28
-------
Qr =
(2-35)
The second source component results from mechanical disturbance of
site surface soil. Mechanical disturbance occurs during a user-specified
interval. Within this interval, the fraction of time per year that the
disturbance occurs is Fmecn. The source term component for mechanical
disturbance is parameterized by the resuspension rate, Rr, having units of
inverse seconds, as
Qmech = CGARrFmech (2-36)
The net source strength for the site is the sum of these components:
Q = Qr + Qmech (2~37)
Transport Formulation - The PRESTO-EPA-POP code uses a Gau,ssian plume
atmospheric transport model, which is an extension of an equation of the
form (S168)
X =
exp
y2
2V
+exp
1 /z+H
(2-38)
This equation describes Gaussian distribution, where X represents the
radionuclide concentration, Q the source strength, and H the corrected
source release height to be discussed later. Dispersion parameters, oy and
CTZ, are the standard deviations of the plume concentration in the horizontal
and vertical directions, respectively. The aerosol is assumed to be trans-
ported at a wind speed (height-independent) u to a sampling position
located at surface elevation z and transverse horizontal distance y from
the plume center. Mass conservation within the plume is insured by
assuming perfect reflection at the ground surface. This is accomplished by
2-29
-------
the use of an image source at an elevation -H, which leads to the presence
of two terms within the braces, and to the factor 1/2. A correction for
plume depletion will be discussed later. Equation (2-38) may be obtained
from any of several reasonable conceptual transport and dispersion models.
Atmospheric transport at several sites of possible interest to
individuals evaluating consequences of low-level waste transport have also
been considered elsewhere. These include Hanford, Washington (Fi81, Mi81),
Savannah River, South Carolina (FiSOb), and Brookhaven, New York (Si66).
Implicit in Equation (2-38) is the assumption that the plume centerline
height is the same as the release height H. In practice, the plume may be
considered to originate at some height, H, with respect to the population
at risk. Some situations, such as the existence of a ridge between the
disposal site and the population centroid, may dictate use of an effective
height greater than H (e.g., the ridge height). The plume thus has an
effective height, Heff, at which the plume may be considered to originate.
This effective value should be used instead of the actual stack height as
the starting point of Gaussian plume calculations. If the particulates in
the effluent have an average gravitational fall velocity, Vg, the plume
centerline will tilt downward with an angle from the horizontal, the
tangent of which is Vg/u. The elevation of the plume centerline at a
distance x downwind is then
H = Heff - xVg/u for H >. 0 (2-39)
and it is this corrected value that is used to compute the aerosol concen-
tration at a distant point.
2-30
-------
Effects of a Stable Air Layer on Transport - The Gaussian plume
formulation has been modified for use in PRESTO-EPA-POP to account for the
presence of a stable air layer at high altitudes. Upward dispersion of the
plume subsequent to release is eventually restricted when the plume
encounters an elevated stable air layer or lid at some height HL. Pasquill
has summarized some reasonable approximations to the modified vertical
concentration profile for various ranges downwind which are used here
(Pa76). The limiting value of az may be defined as
<7z(1imit) = 2(HL - H)/2.15 (2-40)
2
This equation follows from setting the ground-level contribution to the
plume from an image source located above the stable air layer to one tenth
the value of the plume concentration. It is assumed that the limiting
value of ffz calculated in this manner is correct for distances beyond this
point. For shorter downwind distances where the vertical dispersion
coefficient O"z is less than crz(limit), the Pasquill-Gifford value ofaz is
used. For greater downwind distances where o"z is greater than or equal to
^(limit), the value of ^(limit) given in Equation (2-40) is used instead.
The lid height is a user-specified value in the PRESTO-EPA-POP code. For
LLW applications, the source height will usually be sufficiently low
that the influence of HL will be small. For some sites, however, the
influence of an intervening ridge may necessitate a larger effective source
height.
Effects of Plume Depletion - The plume is depleted at ground level
during travel as the particulates are deposited. Both fallout and
electrochemical deposition may be important considerations, and ground
2-31
-------
cover characteristics are of major importance. Under certain obvious
conditions, washout is also of importance, but those conditions have not
been included within this model. Fallout is partially quantified in the Vg
term defined earlier. Near ground level the deposition process is often
characterized by a deposition velocity Vd (Gif62, Mu76a, Mu76b). The
deposition rate W is defined by
W = Vd X (2-41)
Where
X = radionuclide concentration in air (Ci/nr).
The magnitude of the plume depletion within the downwind sector may be
found by integrating across the plume. Using Equation (2-38) and setting
z = 0 it is found that
£ /"- M*
-co
- exp
- y2
H2"
- M Hy
2(7Z2
co -~ -, (2-42)
-co
By performing the indicated quadrature across the plume and further
integrating along the longitudinal direction to express the loss of release
agent as a multiplicative factor, it can be shown (Mi78) that the ratio of
the air concentration considering deposition processes, Xd, to the air
concentration without regarding deposition, X, is
dx (2-43)
f *L /"-I exp ["-
T u J °z L
2-32
-------
Since (Tz is a complicated empirical function of x, Equation (2-43) must be
evaluated numerically.
In the PRESTO-EPA-POP applications, the average value of radionuclide
concentration X, across a 22.5-degree downwind sector is the desired
quantity. In this case, the trans-sector integration leads to the value
2.032 in the air concentration equation (Cu76). This value includes the
1/27T factor in Equation (2-38).
In conclusion, assuming that the radionuclide distribution is that of
a Gaussian plume, we may compute the mean radionuclide concentration, X, at
ground level for the 22.5-degree downwind sector by
x = 2.032FdFwQ
uxO".
exp
z
H'
20 2
(2-44)
z
The value of H in Equation (2-44) must be an effective source height.
This value is corrected in PRESTO-EPA-POP for plume tilt as in Equation
(2-39) and the accompanying discussion. For use in the PRESTO-EPA-POP code,
H is on the order of 1 m for reasonably flat sites, but in many cases other
values should be used to account for local site characteristics, e.g., for
the presence of updrafts.
It has been noted that the choice of plume dispersion parameter o"z is
a user option in the PRESTO-EPA-POP code. Choice of appropriate parameter-
ization depends on site meteorology, topography, and release conditions.
The DWNWND code (FiSOa), which has been included as part of PRESTO-EPA-POP,
includes a choice of eight parameterization schemes for plume dispersion and
a choice of six stability classifications. The most often used dispersion
parameterization scheme for the Gaussian plume is the Pasquill-Gifford
2-33
-------
model. This is the approach most appropriate for long-term LLW assessment
calculations. Likewise, unless site-specific meteorology dictates otherwise,
the D stability category, denoting a neutral atmosphere, should be used.
Pasquill (Pa61, Pa74) considered ground level emission tracer studies
and wind-direction fluctuation data and developed dispersion parameter!'za-
tions for six atmospheric stability classes ranging from A, most unstable,
through F, most stable. Pasquill's values are approximate for ground level
emissions of low surface roughness (Vo77). These values were devised for
small source distances (<1 km). The so-called Pasquil1-Gifford form of
this parameterization (Hi62) has been tabulated by Culkowski and Patterson
(Cu76), and are used in this model.
2.1.3 Food Chain Calculations
Mean concentrations of radionuclides in air, stream water, and well
water are calculated by the equations listed in Sections 2.1.1 and 2.1.2.
This section describes how radionucl ides in those and other environmental
media are used to calculate human internal exposure and potential health
effects.
Radionuclides in water may impact humans by internal exposure,
directly from use of drinking water or indirectly from use of irrigation
water used for crops. Radionuclides in air may impact humans by either
external or internal radiological doses. External doses may result from
immersion in a plume of contaminated air or by exposure to soil surfaces
contaminated by deposition from the plume. Internal doses may result from
inhalation of contaminated air or ingestion of food products contaminated
2-34
-------
by deposition from the plume. Dose and health effects calculations are
made by the DARTAB program (Be81) which is utilized as a subroutine in
PRESTO-EPA-POP. DARTAB will be discussed in some detail later.
Radionuclide input to DARTAB consists of the constant concentrations in air
(person-Ci/m3), constant concentrations on ground surface (person-Ci/m2) ,
constant collective ingestion rate (person-pCi/yr) and constant collective
inhalation rate (person-pCi/yr) . Calculation of each of these by
PRESTO-EPA-POP will be discussed next.
Concentrations of radionucl ides in air which affect the population or
an individual are calculated as described in Section 2.1.2. It is assumed
that the mean nuclide concentrations in air are constant during the total
period of the simulation, as required, for input to DARTAB.
Concentration of each radionucl ide on the ground surface, Qs(pCi/m2)
is calculated using
Qs = CSP + CSPO (2-45)
where
Qs = concentration of radionucl ide on the ground surface at the
populated area of interest
CSP = radionucl ide concentration in the soil used for farming due to
atmospheric deposition
CSPO = radionuclide concentration in the soil used for farming due to
irrigation (pCi/m2)
Appropriate unit conversions are made within the code.
The collective inhalation rate is calculated by multiplying the
population size by the generic individual inhalation rate of
radionucl ides.
2-35
-------
Qinh = Ua CA (2-46)
where
Qinh = Ci
Ua = inhalation rate (m^/yr)
"C)\ = mean ground level radionuclide concentration at a point of
interest (Ci/m^)
The units of Q-jnn are converted to person pCi/yr for input to the DARTAB
subroutine.
The collective ingestion rate is the input to DARTAB that requires the
most calculations by PRESTO-EPA-POP. Ingestion includes intake of drinking
water, beef, milk, and crops. Except for drinking water, all of these
media may be contaminated by either atmospheric processes or by irrigation.
The atmospheric deposition rate onto food surfaces or soil that is
used in subsequent calculation of radionuclide content in the food chain is
d = 3.6X1015 (TAVd (2-47)
where
d = mean rate of radionuclide deposition onto ground or plant
surfaces (pCi/m^ hr)
CA = mean ground level radionuclide concentration at point of
interest (Ci/m^)
3.6X1015 = sec-pCi/hr-Ci
Vd = deposition velocity (m/sec)
The following equation estimates the concentration ITV of a given
nuclide in and on vegetation at the deposited location (except for H-3 and
C-14):
2-36
-------
Yv Xe
where Tv is measured in pCi/kg, d is defined as above, and
R = the fraction of deposited activity retained on crops (unitless)
Xe = effective removal rate constant for the radionucl i'de from crops
(hr~l), where Xe = X+XW, is the radioactive decay constant
andXw is the removal rate constant for physical loss by
weatheri ng
te = the time period that crops are exposed to contamination during
the growing season (hr)
Yv = the agricultural productivity or yield [kg (wet weight)/m2]
B = the radionucl ide concentration factor for uptake from soil by
edible parts of crops, [pCi/kg (dry weight) per pCi/kg dry soil ]
CSP = soil radionuclide concentration updated yearly
P = the effective surface density for topsoil [kg(dry soil)/m2]
tn = time interval between harvest and consumption of the food (hr)
CSP = (CSPL+dAt)exp[At(-X-X s)]
where
CSP = soil radionuclide concentration for this year
CSPL = soil radionuclide concentration for last year
«
d = mean rate of radionuclide deposition
X = radioactive decay constant (yr~l)
Xs = rate constant for contaminant removal
At = time increment, equal to one year in PRESTO model
If farming is performed on the trench site, then the soil radionuclide
concentration is calculated as
SOCON =
2-37
-------
where
SOCON = soil radionuclide concentration (pCi/m2)
SD = depth of contaminated surface region (m)
C$ = radionuclide concentration in interstitial water of contaminated
surface region (Ci/m3)
W$ = porosity of surface soil (unitless)
C§ = radionuclide concentration in soil of contaminated surface
region (Ci/kg)
PS = bulk density of surface soil (g/cm3)
1012 = pCi/Ci
in3 = -kj- . cm^
g m3
The rate constant for contaminant removal from the soil, Rs, is estimated
using
where
Xs = removal rate coefficient (hr~l)
rs = watershed infiltration (m/yr)
PS = soil bulk density (g/cm3)
Kfj = distribution coefficient (ml/g)
Ws = porosity (unitless)
0.15 = depth of soil layer (m)
8760 = hr/yr
Equation (2-48) is used to estimate radionuclide concentrations in
produce and leafy vegetables consumed by humans and in forage (pasture
grass or stored feed) consumed by dairy cows, beef cattle, or goats.
2-38
-------
The concentration of each radionucl ide in animal forage is calculated
by use of the equation
cf =fpfscp + d-Vs)Cs (2-50)
where
Cf = the radionuclide concentration in the animal's feed (pCi/kg)
Cp = the radionuclide concentration on pasture grass (pCi/kg),
calculated using Equation (2-48) with tn = 0
Cs = the radionuclide concentration in stored feeds in pCi/kg,
calculated using Equation (2-48) with t^ = 2160 hr or 90 days
fp = the fraction of the year that animals graze on pasture
(unitless)
fs = the fraction of daily feed that is pasture grass when the
animals graze on pasture (unitless)
The concentration of each radionuclide in milk is estimated as
Cm = FmCfQfexp(-Xtf) (2-51)
where
Cm = the radionuclide concentration per liter in milk (pCi/1)
Cf = the radionuclide concentration in the animal's feed (pCi/kg)
Fm = the average fraction of the animal's daily intake of a given
radionuclide which appears in each liter of milk (d/1)
Qf = the amount of feed consumed by the animal per day (wet kg/d)
tf = the average transport time of the activity from the feed into
the milk and to the receptor (hr)
X = the radiological decay constant (hr~l)
The radionuclide concentration in meat from atmospheric deposition
depends, as with milk, on the amount of feed consumed and its level of
contamination. The radionuclide concentration in meat is estimated using
2-39
-------
CF = FfCfQfexp(-Xts) (2-52)
where
Cp = the nuclide concentration in animal flesh (pCi/kg)
Ff = the fraction of the animal's daily intake of a given radio-
nuclide which appears in each kilogram of flesh (d/kg)
Cf = the concentration of radionuclide in the animal's feed (pCi/kg)
Qf = the amount of feed consumed by the animal per day (kg/d)
ts = the average time from slaughter to consumption (hr)
Concentrations of radionuclides in foodstuffs that result from spray
irrigation with contaminated water are estimated using essentially the same
equations as for atmospheric deposition with the following differences:
the concentration in vegetation, TTV is estimated using Equation (2-48), but
a different value of the retention fraction, R, is used. For irrigation,
the second term of Equation (2-48) is modified by a factor of fj, fraction
of the year during which irrigation occurs and the te in the exponent
becomes tw, equivalent to fj in hours. For irrigation calculations, the
deposition rate, d, in Equation (2-48) becomes the irrigation rate, Ir,
expressed as
IP = Cw K! (2-53)
where
IP = radionuclide application rate (pCi/m2 hr)
Cw = radionuclide concentration in irrigation water (pCi/1)
MI = irrigation rate (l/m2
The concentration in water, Cw, is an average of well and stream water
weighted by the respective amounts of each that are used.
2-40
-------
Another modification introduced for irrigation calculations is related
to the radionuclide concentration in milk and meat where animal's intake of
water was added to Equation (2-51) and (2-52), respectively. This becomes
cm = Fm(CfVcw Qw)exp(-Xtf) (2-54)
CF = Ff(CfQf+Cw Qw)exp(-Xts) (2-55)
where
Qw = the amount of water consumed by the animal each day (1/d)
Once radionuclide concentrations in all the various foodstuffs are
calculated, the annual ingestion rate for each radionuclide is estimated by
Qing = Qv + Qmilk + Qmeat + QW (2-56)
where the variables represent individual annual intakes of a given radio-
nuclide via total ingestion, Q-jng> ancl ingestion of vegetation, Qv, milk,
Qmilk' meat» Qmeat' anc' drinking water, Qw, respectively, in pCi/yr. The
annual intakes via each type of food, Qv for instance, are calculated as
Qv = (CV+CV) Uv (2-57)
where
Qv = annual radionuclide intake from vegetation (pCi/yr)
CY = radionuclide concentration in vegetation from irrigation
(pCi/kg)
CY = radionuclide concentration in vegetation from atmospheric
deposition (pCi/kg)
Uv = individual annual intake of vegetation (kg/yr)
2-41
-------
To satisfy the input requirements for DARTAB, the annual individual
intakes are multiplied by the size of the population to calculate the
collective ingestion annually.
As mentioned earlier, Equations (2-47) through (2-55) do not apply
directly to calculations of concentrations of H-3 or C-14 in foodstuffs.
For application of tritium in irrigation water, it is assumed that the
concentration in all vegetation Cv is the same as the tritium concentration
in drinking water; therefore
Cv = Cw (2-58)
where Cv and Cw are in pCi/kg and pCi/1, respectively. The concentration
of H-3 in animal's feed, Cf, is therefore also equal to Cw. Then, from
Equations (2-54) and (2-55), the concentration of tritium in animal's milk
and meat can be written as
Cm = FmCw(Qf+Qw) (2-59)
CF = FfCw(Qf+Qw) (2-60)
where
Cm = concentration of tritium in milk (pCi/1)
Fm = fraction of the animal's daily intake of H-3 that appears in
each liter of milk (days/1)
Cw = H-3 concentration in animal drinking water (pCi/1)
Qf = animal's daily intake of forage (kg/d)
Qw = cow's daily intake of water (1/d)
Cp = concentration of tritium in animal meat (pCi/kg)
Ff = fraction of the animal's daily intake of H-3 that appears in
each kg of meat (d/kg)
2-42
-------
The exponential term is neglected due to the relatively long half life of
tritium as compared to transit times in the food chain.
The root uptake of C-14 from irrigation water is considered negligible
and, therefore, has been set equal to zero.
For vegetation contaminated by atmospheric deposition of tritium, H-3
concentrations are calculated by
Cv = ^ (0.75)(0.5)(lxlOl5) (2-61)
h
where
Cv = H-3 concentration in vegetation (pCi/kg)
C/\ = concentration of H-3 in air (Ci/m^)
h = absolute humidity of the atmosphere (g/m3)
0.75 = ratio of H-3 concentration in plant water to that in
atmospheric water
0.5 = ratio of H-3 concentration in atmospheric water to total
H-3 concentration in atmosphere.
IxlO15 - (lx!012pCi/Ci)x(103g/kg)
The mean ground level air concentration of H-3, C^, is calculated using
equations in Section 2.1.2.
For C-14, the concentration in vegetation is calculated assuming that
the ratio of C-14 to be the natural carbon in vegetation is the same as
that ratio in the surrounding atmosphere. The concentration of C-14 is
given by
Cv = CAT_ (O.il)(lxl015) (2-62)
0.16
2-43
-------
where
Cv = C-14 concentration in vegetation (pCi/kg)
C/\ = mean ground-level concentration of C-14 in air (Ci/m3), also
calculated from equations given in Section 2.1.2
r = ratio of the total release time of C-14 to the total annual
time during which photosynthesis occurs, r
-------
where Kj contains any numerical factors introduced by the units of E-jj(k),
the exposure to the ith radionucl ide in the jth pathway, DF-jj] is the dose
rate factor of the ith radionuclide, the jth pathway and the 1th organ, and
P(k) is the exposed population at location k. Note that all E-JJ and DF-jj]
for various nuclides (index i) and organs (index 1) have consistent units.
DARTAB performs three calculations and tabulations for dose rate and
dose: (1) dose rate to an individual at a selected location, (2) dose rate
to a mean or average individual, and (3) collective population dose rate.
Table 2-2 lists units of DF-jj] and E-JJ for each of the four pathways for
selected individual dose calculations. Dose rates, D-j ,-] , are in mrad/yr.
Mean individual dose rates are calculated using
? P(k) Dij^k)
D11.JL__
Note that in PRESTO-EPA-POP the impacted population is considered to reside
at only one location (k = 1). Hence, calculations of mean individual dose
rate are numerically equivalent to the sum of pathway doses for the
selected individual dose rate. The collective dose rate for the exposed
population is the product of D-JJ] and the number of persons exposed. Units
of the collective dose rate are person rad/yr.
The above dose rates may be expressed in a number of different combina-
tions. The doses can be summed directly over pathways:
Dji(k) = EDij^k) (2-65)
j
or over all nuclides:
2-45
-------
TABLE 2-2
UNITS OF EXPOSURE FACTOR Eij, AND DOSE RATE FACTOR, DFi-p
FOR SELECTED INDIVIDUAL DOSE RATE CALCULATIONS BY DARTAB
Unit of Factor
Pathway
Ingestion
Inhalation
Air Immersion
Ground Surface Exposure
1j
DF
ij1
(person-pCi )/yr
(person-pCi )/yr
(person-pCi }/m?
(person-pCi )/m2
(mrad/yr)/(pCi/yr )
(mrad/yr)/(pd'/yr)
(mrad/yr)/(pCi/m^)
(mrad/yr)
2-46
-------
Djl(k) = E DijTfk) (2-66)
i
The total dose to the 1th organ at location k, D (k), is then
D!(k) = E £ Di-pfk) (2-67)
j i
The dose equivalent (mrem), H, for the 1th organ is given as
H](k) = QF(iow-LET)Dl(low-LET)+QF(high-LET)Dl(k,high-LET) (2-68)
where QF denotes the relative biological effect factor. The factor is
defined for each organ or health effect.
To combine dose rates to different organs, a weighted sum is used
Dij(k) = EVlTDi-pfk) (2-69)
where W] are weighting factors for the various organ doses supplied by the
user where
£ Wi = 1 (2-70)
1
Weighting factors developed by EPA for the various organs were used as
input into DARTAB. The International Commission on Radiological Protection
(ICRP79) has proposed a similar approach to adding organ doses.
Health Effects Estimates - The health effects and risk equivalent are
computed in a manner similar to the dose calculations. The health effects
or individual risk of premature death to an individual at location k for
the 1th cancer, ith radionuclide, and jth exposure pathway is given by
Rijl(k) = 10-5KjEij(k)RF1jl/P(k) (2-71)
2-47
-------
where K-; again serves to reconcile the units of E-jj(k) and RF-jj]. The
total individual risk represented by the exposure and intakes of all
radionucl ides through all pathways is given as
R(k) - 10-5 £Kj £ Eij(k) £ RFi-p/Pfk) (2-72)
j i i
and the health effects can be summed over pathways, radionucl ides , or
cancers. The mean or average individual risk is estimated in a similar
way.
The collective health effects are expressed as the health effects
rate. For example, the total equilibrium fatal cancer rate in an exposed
population is
HE = ^^EKj E EE-j-U)!; RFi-M (2-73)
Te j k 1 1
where Te is the mean individual lifetime (70. 7y)
In DARTAB, life loss (years) per premature death is calculated by
^Kj f Eij(k)YLijl
=J-Aj - L_ - 1±L (2-74)
where
YI(|<) = average life lost (years) per premature death from cancer 1 at
location k
YL-jji = total life lost (years) for unit exposure to nuclide i, pathway
j, and cancer 1
ij(k) = is the exposure to or intake rate of the ith radionuclide
through the jth exposure or intake mode at location k in the
envi ronment
2-48
-------
= the mortality risk factor per unit exposure or intake rate of
the ith radionuclide in the jth exposure or intake mode for the
1th cancer site
The factor Kj converts any pathway specific units to the required
units. Note then that the numerator is j.ust the total years of life lost
by those experiencing a cancer of the 1th organ, while the denominator is
the total number of deaths due to radiation induced cancers of the 1th organ.
DARTAB performs two calculations and tabulations of life loss per
premature death (1) life loss per premature death for an individual at a
selected location and (2) life loss per premature death for a mean or
average individual. Table 2-3 lists units of the exposure, loss of life,
and risk mortality factors.
The mean individual life loss per premature death estimate, Y], is
merely the sum over all locations, k, of Y-|(k) calculated using
Equation (2-74). As with the dose calculations, it should be noted that
PRESTO-EPA-POP assumes that the total population resides at one location,
k = 1. Therefore, mean individual premature death values are equivalent to
those for the selected individual.
Readers desiring a complete discussion of the development of the dose,
health effect, or risk equivalent factors utilized by DARTAB should consult
the DARTAB documentation report (Be81, pp. 5-10) or the supporting report
(Du80). The latter describes the theory and development of the RADRISK
code that generates the risk factors utilized by DARTAB.
2.2.2 Estimation of Basement Dose to Resident Intruder
The DARTAB subroutine of the PRESTO-EPA-POP model contains algorithms
to compute the dose rate per unit radionuclide surface concentration to an
2-49
-------
TABLE 2-3
UNITS OF YEARS LOST FACTOR, Yl^-p, AND MORTALITY RISK FACTOR,
FOR HEALTH RISK CALCULATIONS BY DARTAB
(Corresponding to Exposure Factors Listed in Table 2-2)
Pathway
Ingestion
Inhalation
Air Immersion
Unit of Factor
YU
RFijl
yr life loss/(pCi/yr) (deaths/105 persons)/(pCi/yr)
yr life loss/(pCi/yr) (deaths/105 persons)/(pCi/yr)
yr life loss/(pCi/m3) (deaths/105 persons)/(pCi/m3)
Ground Surface Exposure yr life loss/(pCi/m2) (deaths/105 persons)/(pCi/m2)
2-50
-------
"individual standing on a contaminated, infinite plane. This section
describes the calculation of a factor which is used to convert the input to
this infinite plane computation so that the calculation computes a value
appropriate for an individual spending part of his time in a basement. In
this calculation it is assumed that the basement actually extends into and
is surrounded by the trench contents. Furthermore, it is assumed that most
of the individual's time is spent at the center of the basement, that the
basement radius is three meters, and that the radiation attenuation
coefficient of the trench may be approximated by that of soil, with
attenuation coefficients taken from literature published by the British
Standard Institute (BSI66). The elapsed time between closure of the waste
disposal area and construction of the basement is an input parameter for
the model .
A conversion factor F is defined which is used to convert the radio-
nuclide concentration in the trench surrounding the basement to a value
appropriate for an input parameter to the infinite plane calculation.
Provided the basement is continuously occupied, this conversion factor is
defined by the equation
F = - (2-75)
Dp/A
where
= dose rate in basement per unit of radionuclide concentration in
trench [(mrad/yr)/(pCi/m3)]
Dp/A = infinite plane dose rate per unit of surface concentration on
ground [(mrad/yr)/(pCi/m2)]
2-51
-------
In Equation (2-75) A represents the radionuclide concentration per unit
surface area on the infinite plane and N represents the radionuclide concen-
tration per unit volume in the trench material. If the value of the factor
F, is known the radionuclide dose rate to an individual within the basement
may be found by using a modified form of the above equation
Db = _EL FN (mrad/yr) (2-76)
A
The basement whole body gamma dose rate per unit of radionuclide
concentration at a distance one meter above the basement floor is found by
integrating the radiation flux from each volume element of the trench
material over the trench volume v
Db = C B(/yT)exp[-(/ya^TrT)]dv (2-77)
NC -'y r2
where
C = units transformation constant [(mrad/yr)/(pCi/m2)]
B(AtTrt) = build up factor, using formulas by Eisenhauer and Simmons
for energies up to 200 kev and Taylor's formula for
energies above 200 kev. Coefficients for the Eisenhauer
and Simmons equation are taken from Eisenhauer and Simmons
(Ei75) and for Taylor's formula are taken from Morgan and
Turner (Mor67)
r = distance from point of interest to element of volume of
the trench dv (m)
)U,a = linear attenuation coefficient of air (m"-'-)
My = linear attenuation coefficient of trench (m~l)
ra = distance in air from point of interest to element of volume
dv (m)
ry = distance in trench from point of interest to element of
volume dv (m)
v = trench volume (m^)
2-52
-------
The basement may be considered circular, so that Equation (2-77)
becomes
/y»
B(/^jrj) r i LL +i r \~\r\ + I D\' \f [/ r ILL +f^-r \ IH
'(floor) r2" 3 J v(waTT) r2
.R+d ,,H+d
ir I r'.^V
J J
(2-78)
o \\
^R+d H
27T/ / r' B(^TrT)pxpr-fMara+/lTrT) IdZdr'
where
R = basement radius (m)
h = distance of point of interest from floor (h = 1m)
H = basement height (m)
d = cut-off thickness of trench, chosen to be 10 mean free paths
(or
The first integrand refers to the section of the trench immediately
below the basement floor, while the second integrand refers to the trench
material outside the walls of the basement. For this calculation, the
basement is assumed circular, and a two-dimensional Simpson's rule method
(McC64) is used to numerically evaluate the integrals.
Equation (2-78) has been evaluated to determine values of the ratio
Ob/Me, and we have found that as the assumed basement radius varies from 3 to
6 m, the completed value of D^/NC changes by only 30 percent (being greater
for the smaller basement radius) for radiation energies ranging from 20 keV
through 10 MeV. Tabulated values of the linear attenuation coefficient for
air (Ko79) and for earth are used (BSI66).
2-53
-------
The dose rate at a height of one meter per unit surface concentration
from an infinite plane is given by the equation
00
= / 1- e"^ar ds = 27T f 1
J r2 V r
dr = 27TI (2-79)
AC
1
where
C = units transformations constant [(mrad/yr)/(pCi/m2)]
oo
I = f 0/r)exp(-Atar)dr (dimensionless)
"1
Aa = linear attenuation coefficient of air (m~l)
z = height of point of interest (z = 1m)
In this transformation, the incremental area element dS is 27TXdX,
where X is the radius projection onto the plane; and since R2 = X2 + 1,
then have XdX=RdR. The value of the integral, I, in this equation, may be
computed numerically using a polynomial approximation (Ga64) for values of
Ma corresponding to different values of gamma energies. The results of
these calculations are summarized in Table 2-4.
The value of the ratio F as defined by Equation (2-75) may be obtained
for a given energy by dividing the results of the basement calculation by the
results of the infinite plane calculation. Values of this ratio for energies
between 10 keV and 10 MeV are given for a basement radius of 3.0 m in
Table 2-4. A very conservative average value of F may be chosen to be 0.1 m.
If the basement is occupied one-third of each day, then the radionuclide
concentration within the trench is one-third. Therefore, the basement
exposure dose rate in the infinite plane dose rate calculation of the
DARTAB subroutine is found by multiplying the average radionuclide concen-
2-54
-------
TABLE 2-4
RESULTS OF BASEMENT AND INFINITE PLANE
UNIT DOSE RATE COMPUTATIONS
Energy
MeV F(m)
0.05 0.015
0.10 0.045
0.20 0.061
0.50 0.087
1.0 0.087
2.0 0.088
4.0 0.092
6.0 0.098
8.0 0.099
10.0 0.101
2-55
-------
tration by the volume within the trench during the basement occupancy
period by the volume to the surface correction term F and the fraction of
time the basement is assumed to be occupied. Thus, the value of A is
augmented by the quantity 0.033N to yield a value that corresponds to the
plane dose plus the basement dose. In the computer code, the time at which
the basement is constructed is a user input parameter, and the average
radionuclide concentration by volume for that period between basement
construction until the end of the simulation period is computed by the
code. This incremental concentration is added to the computed average
surface concentration if the code user has elected to include the basement
exposure mode.
2.2.3 Accounting for Radioactive Decay Products
The code does not account for ingrowth of radioactive decay products
of materials during storage in the trench or during environmental transport
following release from the trench. The RADRISK data files accessed by
DARTAB do, however, include dose and risk factors that account for such
ingrowth and subsequent exposure after materials have entered the human
body. In cases where the radioactive decay product is short-lived relative
to the parent, the radionuclide concentrations calculated for an
environmental media may be in error because of this ingrowth.
For example, when cesium-137 (half-life = 30 yr) is included in trench
inventory, barium-137m (half-life = 2.55 min) should be in secular equilib-
rium with the parent nuclide. If Ba-137m is not listed as part of the
trench inventory, then no environmental concentrations will be calculated.
Therefore, external exposures will be underestimated because of the absence
of the 0.662 MeV barium-137m gamma rays. The internal exposures will
include the exposure to these gamma rays as noted above.
2-56
-------
In situations where external exposures may be important, the user may
include the radioactive decay products in the initial trench inventory. In
such cases, the radioactive decay products should be entered with the same
activity, decay coefficient, and environmental transport parameters as the
parent. The effect of secular equilibrium will be achieved throughout
transport in the environment. The fact that cesium and barium probably do
not have identical chemical and environmental behavior will be relatively
unimportant because of the short half-life of the progeny. Entering the
decay product in the source term in such a manner will not grossly
overestimate internal exposures because the dynamics of the decay products
inside a human body tend to result in low doses. In particular, this is
true because the RADRISK data base, which contains risk factors used by
DARTAB, will not be affected by the decay rate of the decay product as
indicated in the environmental transport portion of the input data set (K.
F. Eckerman, Oak Ridge National Laboratory, personal communication).
2.3 HEALTH EFFECTS TO REGIONAL BASIN POPULATION
The PRESTO-EPA-POP model evaluates the cumulative health effects to
the population of a regional basin downstream from the disposal site for a
period of 10,000 years after site closure. Because of the uncertainties in
predicting health effects over long periods of time, and to reduce the
computer costs, the analysis is divided in two parts, the primary analysis
and the basin analysis. The primary analysis, for 1000 years, simulates
the health effects to the local community as described in the previous
sections.
2-57
-------
Those radionuclides not used or consumed by the local community during
the first 1000 years are considered to be residual radionuclides. In
addition, after the 1000 year local assessment period has ended, all
radionuclides that leave the disposal site and enter the regional basin
(which now incorporates the local area, see Figure 2-4) are considered
residual radionuclides. In the regional basin analysis, health effects to
a regional basin population are calculated for 10,000 years for all
residual radionuclides entering the downstream regional basin, using health
effects conversion factors. The total health effects are equal to the sum
of the health effects obtained from the primary analysis and the regional
basin analysis (see Figure 2-4).
The regional basin analysis assumes that all of the communities
located in a regional water basin downstream from the disposal site,
including the community analyzed in the primary analysis, can be combined
into a single composite community. The transport of radionuclides from the
disposal site, through the hydrologic pathway, continues as described for
the primary analysis. The atmospheric transport pathway is not included,
since it is assumed that the health effects to a more distant regional
basin from this pathway will be negligible.
Instead of performing lengthy food chain simulations and health
effects analyses for 10,000 years, the model calculates the impact on the
basin based on the "residual radionuclides" released downstream. Residual
radionuclides are the sum of those nuclides released from the LLW site
which are not used by the local community during the primary analysis and
the radionuclides released to the downstream basin during the period of
regional basin analysis. The radionuclides considered are those that enter
2-58
-------
YEARS 1 - 1,000
AQUIFER
YEARS 1,001 - 10,000
LOCAL STREAM S
AQUFER
BASIN RESIDUAL RADIOACTIVITY:
B(CO=CA-W) + (
REGIONAL BASW HEALTH EFFECTS:
HE = BxHECF
- Y)
BASIN RESIDUAL RADIOACTIVITY:
B(co = D + S
REGIONAL BASW HEALTH EFFECTS:
HE = BxHECF
RAE-102208
FIGURE 2-4. REGIONAL BASIN HEALTH EFFECTS PATHWAY.
2-59
-------
the aquifer through the trench bottom and those that enter the regional
stream by way of runoff.
In order to determine the health effects to the regional basin
population, the residual radionuclide activity released to the regional
basin is multiplied by a conversion factor Recalculated for each radio-
nuclide within PRESTO-EPA-POP code. The conversion factors, which are
nuclide dependent, are based on local water use characteristics and the
hydro!ogic pathway.
2.3.1 Calculations of Regional Basin Health Effects
The code uses health effects conversion factors (see Section 2.3.2) to
calculate the health effects to the regional basin population from the
basin residual radionuclides. The basin residual radionuclides consist of
all the radionuclides that leave the disposal site area through the surface
and underground water pathways but are not used by the local population and
go on to enter a major basin stream. Once the radionuclides arrive at the
basin stream, they are released to the basin within the same year of
arrival. Radionuclides not used by the regional basin community are assumed
to travel to the ocean where they contribute no health effects.
Releases of radionuclides to the regional basin can be simulated for
up to 10,000 years. The annual nuclide releases to the regional basin are
collected in the model in ten periods of 1,000 years each. The annual
releases of each nuclide from surface runoff and the aquifer to the regional
basin during the first millenium are collected in the array variable QDWSB.
Nuclides that leave the bottom of the trench during the first millenium and
arrive at the well beyond year 1000 are not neglected; they are also
considered in the yearly loop.
2-60
-------
In each of the first thousand years of simulation, the amount released
to the basin, SSTREM(N), is decreased by the amount of nuclides removed
from the nearby stream(s) with water used by the local population. This
correction is accomplished using the stream flow rate, STFLOW; the
hypothetical volume of water withdrawn from the stream, VOLUSS; and the
stream water concentration, STCON(N). The nuclide release to the basin in
each year of the first millenium is
|(STFLOW - VOLUSS) STCON(N) if VOLUSS < STFLOW (2-80)
I 0 if VOLUSS _> STFLOW
To calculate radionuclide contributions from the aquifer to the basin,
it is necessary to evaluate additional radionuclide transit times as well
as Hung's correction factors for the reach from the well to the stream.
The user can also control the percentage of well water that flows to the
basin stream by specifying the input parameter CPRJ as the fraction of
groundwater that bypasses the basin stream.
The surface soil and surface water concentrations are calculated every
year according to Equations (2-25) and (2-26). These concentrations also
change from year to year as a result of wind resuspension of radionuclides,
water runoff, trench water overflow, the seepage of water from the disposal
site surface to the aquifer. The amount of radionuclides released from the
surface soil of the disposal site to the surrounding surface streams is
calculated using the current year surface water nuclide concentration,
Cy (Ci/m^); the area of the disposal site, S^S] (m^); the annual precipita-
tion rate, Pa (m/yr); the current year amount of trench water overflow,
VQ (m^/yr); and a transfer factor, fr, as follows
2-61
-------
Ws = Mpa SwW (2-81)
SSTREM = Us Cw (2-82)
where Ws (rn^/yr) is the amount of water that enters the surrounding streams
from runoff and trench overflow during the current year of simulation, and
SSTREM (Ci/yr) is the amount of nuclides going along with that volume of
water. The surrounding streams in turn will transport the nuclides to the
regional basin stream within the same current year of simulation.
The total release of radionuclide, QLBTTH, to the basin is the sum of
the 10,000 yr releases, i.e.,
9
QLBTTH = QDWSB + EQLB(J) (2-83)
J = l
The population health effects in the regional basin due to the release
of residual radionucl ides to the basin are calculated by multiplying the
total release of the radionucl ide to the regional basin by a conversion
factor, i.e.,
HE = QLBTTH-CON (2-84).
When a unit response approach is used, the total health effects for
the actual concentration of the waste are calculated in a separate health
effects accounting model. Since the water usage for each water basin is
different from one site to another, different health effect conversion
factors should be used. A detailed description of the health effects
accounting model is discussed in a separate report on the characterization
of health risks and disposal costs associated with alternative methods for
2-62
-------
land disposal (EEI84). The health effects conversion factors, which are
used to determine the health effects to the regional basin population from
residual radionuclides, are calculated independently of PRESTO-EPA-POP.
However, the methodology associated with their derivation is included in
the following section.
2.3.2 Conversion Factors for Regional Basin Health Effects
The health effect and genetic effect conversion factors are used to
calculate the impacts of residual radioactivity entering a regional surface
water drainage basin system. A number of assumptions must be made
concerning the quantity of water contaminated with residual radioactivity
which will be withdrawn by downstream communities, the population using the
stream water, and the uses to which the water will be put (i.e., drinking,
irrigation, etc.). These conversion factors are applied to the residual
radioactivity entering the basin to obtain the number of health effect and
genetic effect.
Per capita water consumption is calculated for each site, taking into
account the local irrigation requirements and the fraction of the year
during which irrigation takes place (Equation (2-85)). For regions where
multiple water sources may be used, fractional correction factors are
applied. For example, a portion of the requirement for the irrigation
water may be met by using a well or stream, while the remainder may be
withdrawn from a farm pond with no contamination. This is handled by
including "switches" in the water consumption equation. Thus if half of
the irrigation water at a given site is withdrawn from a stream while the
rest is gathered from precipitation-fed farm ponds, the irrigation pathway
switch will equal 0.5.
2-63
-------
Vu = [3.9x10^^ + UwLh + 1.5xlo4La]Np (2-85)
where
Vu = water used (1)
3.9xl07 = 4492 m2 irrigated land per person x 8760 hr/yr
W-j = irrigation rate (l/m^-yr)
f-j = fraction of year when irrigating
L-j = irrigating pathway switch
Uw = individual water consumption per year (1/person-yr)
Ln = human pathway switch
1.5xl04 = annual water fed to cattle consumed by humans (1/person-yr)
La = animal pathway switch
Np = size of population
In order to match the per capita water use patterns of the downstream,
basin population to those of the local population, fractional usage para-
meters must be included. For the actual PRESTO-EPA-POP analyses, fractional
usages are modeled for sites where no water use comes from the well or stream.
The annual per capita water usage by the regional basin population is given
by
(Vu/Np)/1000 = per capita water consumption (m^/person-yr)
It is assumed that the regional basin population downstream of the
disposal site is directly related to the volume flow rate in the stream.
An average river basin generally has an annual river flow-to-population
ratio of 3000 m^/person. The site-specific water usage rate (per person)
is then compared to the standard rate of 3000 cubic meters/person-yr to
determine the fraction of stream flow that will be used by the downstream
populations.
2-64
-------
HECFW =
GECFW =
HE
WW + SW
GE
WW + SW
[Surface Water 1 _ per person site-specific water consumption rate /,, Rfi\
Utilization Factor) = standard rate (3000 m3/person-yr)
When the water utilization fraction has been computed, it is used to
compute the number of health effects occurring in the downstream populations.
For each disposal site, output data from PRESTO-EPA-POP are analyzed to
determine the number of health effects and genetic effects occurring in the
local population per curie of each radionuclide pumped from the well or
stream. The water pathway conversion factors are defined as follows:
F (2-87)
F -(2-88)
where
HECF^ = health effect conversion factor for the water pathway
(deaths/Ci)
GECFy = genetic effect conversion factor for the water pathway
(effects/Ci)
HE = number of fatal cancers in the local population over 1000 years
GE = number of genetic effects occurring in the local population
over 1000 years
WW = radioactivity pumped from the well over 1000 years (Ci)
SW = radioactivity pumped from the stream over 1000 years (Ci)
F = surface water utilization factor
For the health effects conversion factor analysis, the air pathway
sources were shut off for the regional basin by setting spillage equal to
zero. No on-site farming or basement exposures are included, either.
Therefore, the health effects in the exposed population are due to use of
contaminated water only.
2-65
-------
In addition to water usage, there is another exposure pathway for the
downstream communities. The possibility exists that contaminated fish will
be consumed by the downstream regional basin population. Conversion
factors for fish consumption (health effects/Ci ) were added to the water
pathway conversion factor, as follows:
HECF = HECFW + HEF (2-89)
GECF = GECFW + GEF
where
HECF = combined health effect conversion factor (effects/Ci)
HEF = health effect conversion factor for consumption of fish
(effects/Ci)
GECF = combined genetic effect conversion factor (effects/Ci)
GEF = genetic effect conversion factor for consumption of fish
(effects/Ci)
The health effect conversion factors for consumption of fish are
calculated in the following manner:
HEFT = ()BfiUi4). (2-90)
GEF-J = (£)BfiUf(£). (2-91)
K LI
where
HEF-j = health risk from fish consumption per curie of nuclide i
released to the river
P = population utilizing the river
R = river flow rate (1/yr)
Bfi = nuclide transfer factor - water to fish (PCl/k9 fish)
pCi/1 water
2-66
-------
Uf = annual fish consumption rate per person
(D/C)-j = cancer risks per curie of nuclide i ingested by the population
GEF-j = genetic effects from fish consumption per curie of nuclide i
released to the river
(G/C)-j = genetic effects per curie of nuclide i ingested by the population
The regional basin health/genetic effects for each nuclide are
calculated by multiplying the residual for the radionuclide released to the
downstream basin by the appropriate health effect or genetic effect
conversion factor, as follows:
Basin Health Effects
[Residual-,- (1st 1000 years) + (2-92)
Residual-j (Years 1001 - 10,000)] HECF-j
Basin Genetic Effects-j
[Residual,- (1st 1000 years) +
Residual-j (Years 1001 - 10,000)]
(2-93)
The total regional basin health/genetic effects resulting from all residual
nuclides are calculated by summing over all nuclides (i) as follows:
N
Total Basin Health Effects = £ Basin Health Effects-;
Total Basin Health Effects =
£
Basin Genetic Effects,
2-67
-------
3. DEVELOPMENT OF PRESTO-EPA-POP CODE
3.1 STRUCTURE AND INFORMATION FLOW
The PRESTO-EPA-POP code is written in FORTRAN IV for an IBM 3081 or
comparable computer system and requires 850K bytes of memory. It is
designed to process up to 40 nuclides for a maximum of 10,000 years.
Evaluation of local and regional basin health effects of 31 radionuclides
over 10,000 years takes approximately 7 minutes to execute. A shorter test
of ten nuclides takes less than two minutes to execute. The program should
be easily transferable to other IBM installations. It has run correctly
on another non-EPA IBM computer system after installation directly from
tape. Non-IBM users may have to modify the job control language (JCL), the
NAMELIST inputs and other program segments where character manipulations
are used.
The PRESTO-EPA-POP code is structured in a modular form to permit
simple upgrading or replacement of given submodels without rewriting the
entire code. The subroutine structure of the code is shown in Figure 3-1.
There are three classes of submodels: unit response, scheduled event,.
and bookkeeping submodels. Unit response submodels simulate processes such
as rainwater infiltration through the intact portion of the trench cap,
erosion of soil overburden from the trench cover, and atmospheric transport.
Such submodels are usually accessed only once during a model run and
generate parameters and rates used elsewhere in the simulation.
3-1
-------
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RAE-102122
FIGURE 3-1. PRESTO-EPA-POP SUBROUTINE STRUCTURE,
3-2
-------
Scheduled event submodels estimate events such as the time of trench
cap failure, while bookkeeping submodels determine the water balance in the
trench and radionuclide concentrations in the trench outflow and the
aquifer. Output from the bookkeeping submodels is iterated annually over
the simulation period. Risk evaluation bookkeeping submodels accept the
cumulative or mean output from the transport portion of the code and
generate doses and population risks, based on a life-table approach.
3.2 SUBROUTINE DESCRIPTION
An alphabetical listing and description of the subroutines and main
program found in PRESTO-EPA-POP is given below.
MAIN - This routine is the main calling program of PRESTO-EPA-POP and
defines the most commonly used variables of the code, specifies dimension
and common areas, and initializes variables and input control parameters.
The input and output subroutines, SOURCE and OUT, are called directly by
MAIN (Figure 3-1), as are the unit response model subroutines AIRTRM, and
ERORF. MAIN also calculates: the vertical water velocity; retardation
factors; vertical, horizontal and total transit times in groundwater (the
transfers from trench to vertical soil column to aquifer in Figure 2-1);
and the basement exposure correction factor (Section 2.2.2). The decay-
dispersion correction factor, DDETA (Hu81), is calculated for each
radionuclide in MAIN (factor DDETA adjusts the activity output of the
aquifer for the combined interactions of longitudinal dispersion and
radioactive decay.) QUANC8, which is based on an eight panel Newton-Cotes
rule, performs the integration necessary to obtain the correction factor.
3-3
-------
MAIN calls the bookkeeping subroutines to calculate quantities associ-
ated with trench water balance, trench cap status, changes in land use and
basement occupancy. Other subroutines called by MAIN compute the amount of
leaching from trench, transport of soluble surface components, atmospheric
concentrations, and well concentrations. In addition, aquifer volume,
hypothetical radionuclide withdrawal from well, and material balances for
water in the aquifer are calculated in MAIN.
Risk evaluation submodels called from MAIN account for radionuclide
concentrations in food due to atmospheric deposition and water irrigation,
and radionuclide intake by man. These subroutines are IRRIG, FOOD, HUMEX,
CV, COV, IRRIGA, FOODA, HUMEXA, CVA, AND COVA. Finally DARTAB, which
creates tables of predicted health effects from radioactive effluents is
called from MAIN.
The annual simulation loop and the radionuclide loop are executed a
selected number of times. During a model run, MAIN may access any or all
of the subroutines or functions which are listed below in alphabetical
order.
Average concentration values printed in the concentration tables are
computed in the MAIN routine using a summation calculation within the MAXYR
loop (the principal yearly iteration loop). After this loop is completed,
the summed concentration values are divided by the number of years considered
in the simulation and the results are printed. Maximum concentration
values are identified by comparing stored concentration values to the
values determined in each iteration of the yearly simulation loop. If the
new concentration is greater, then the concentration and corresponding year
number are stored for printing in the concentration tables.
3-4
-------
AIRTRM - This subroutine is the main calling program for the
atmospheric transport submodel. AIRTRM calculates sector-averaged (22.5
degree) atmospheric exposures normalized to the source strength. AIRTRM
and all its supporting subroutines are adaptations of the interactive
Gaussian plume atmospheric model, DWNWND (FiSOa). AIRTRM also calculates
the deposition rate onto surfaces per unit source strength. To-make these
calculations, AIRTRM accesses four other subroutines, SIGMAZ, DPLT, YLAG,
and SIMPUN, and utilizes a number of user-input parameters including source
height, lid height, stability class, type of stability class formulation,
Hosker roughness parameter, wind velocity, deposition velocity, gravitational
fall velocity, and source to receptor distance. The normalized atmospheric
exposures are returned to the main program and are used in later dose and
risk calculations.
CAP - This function calculates and returns to both MAIN and TRENCH,
the fraction of the trench cap that has failed. Cap failure may be either
partial or total. Total failure may be caused by erosion of all overburden
as calculated by ERORF. Partial failure indicates that a portion of the
cap has been completely removed; the remainder of the cap is still subject
to erosion. Partial failure may be caused by user input of the end points
of a linear function to selectively remove all overburden from a fraction
of the trench.
COV, COVA - These functions are called by subroutine IRRIG and IRRIGA
to calculate radionuclide concentrations in vegetables, milk, and meat that
may be contaminated by irrigation. The radionuclide concentrations in food
depend on such quantities as the agricultural productivity of vegetation,
the period of irrigation annually, the storage delay period between harvest
3-5
-------
and use for pasture grass, feed, leafy vegetables and produce, and the
radionuclide decay constant.
CV, CVA - These functions are utilized by subroutines FOOD and FOODA
to calculate radionuclide concentrations in pasture grass and stored feed
consumed by animals, and in leafy vegetables and produce consumed by humans.
CV is essentially the same as function COV, except that CV is used for
atmospherically deposited radionuclides and COV accounts for radionuclides
deposited by spray irrigation. Pertinent input data include agricultural
productivity, fraction of the year vegetation is exposed to depositing
radionuclides, and the delay time between harvest and consumption for
stored feed, pasture grass, leafy vegetables, and produce.
DARTAB - The original DARTAB code is a self-contained program which
combines radionuclide environmental exposure data with dosimetric and
health effects data to create tables of predicted impacts of radioactive
effluents. DARTAB has eleven subroutines and contains over 3000 FORTRAN
source statements. DARTAB subroutines are RDSTOR, FACOUT, CHLOC, PREPDR,
PREPRF, PREPHR, MULT, DRTAB, ORGFAC, SUMMRY, and SUMMR2. These are not
discussed specifically in this report. For information on the original
DARTAB consult the document describing the code (Be81). DARTAB has been
modified for PRESTO-EPA-POP so that the program is treated as a subroutine.
Environmental exposure data are now passed in COMMON from MAIN to DARTAB's
subroutines.
DARTAB uses dosimetric and health effects data from the methodologies
of RADRISK (Du80). RADRISK uses a life-table model to calculate the human
health risk to a cohort of 100,000 people from a constant input of 1 pCi/yr
(0.037 Bq/yr) via ingestion and inhalation over a lifetime (70.7 yr).
3-6
-------
These intake conditions are approximated in PRESTO-EPA-POP by
calculating an average intake over the span of the assessment of each type
of intake. RADRISK data files are accessed directly by DARTAB.
DPLT - The subroutine DPLT is called by AIRTRM and computes a correc-
tion factor for plume depletion. To make this calculation, DPLT calls
subroutines SIGMAZ and SIMPUN.
ERORF - This subroutine uses the universal soil loss equation, USLE,
developed by the U.S. Department of Agriculture (USDA61) to determine
sediment loading for rain-driven surface erosion. Estimation methods and
tabulations for factors used in USLE have been published (McE76). The code
user inputs all six of these factor values. The calculated erosion rate is
returned to MAIN where it is converted to an annual erosion rate in meters.
This erosion rate is utilized by MAIN to determine the thickness of the
cap.
FCN - This function subprogram returns to QUANC8 a functional
evaluation of the integral used in calculation of the aquifer decay-
dispersion correction factor. The routine is written in double precision
to facilitate interaction with the double precision routine QUANC8.
FOOD, FOODA - Subroutine FOOD is called only once per simulation and
calculates the average concentration of each radionuclide in foods
contaminated by atmospheric deposition and root uptake. The deposition
input to FOOD is calculated in subroutine AIRTRM. The equations and
3-7
-------
internal parameters used by FOOD are those in AIRDOS-EPA (Moo79). Output
from FOOD is used by the subroutine HUMEX to calculate the human exposure
via ingestion of these contaminated foodstuffs. Subroutine FOODA is called
from MAIN each simulation year.
HUMEX, HUMEXA - Subroutine HUMEX accepts user input and receives
averaged data from subroutines AIRTRM, FOOD, IRRIG, and VERHOR to calculate
the average annual human exposures via ingestion and inhalation. Output
from HUMEX supplies the input to the DARTAB subroutines for calculations of
risk and dose and tabulation of health results. Subroutine HUMEXA is
called from MAIN each simulation year.
INFIL - The subroutine INFIL is based on a model by Hung (Hu83b) and
calculates annual infiltration through the trench cap. INFIL calls
subroutine SOIL and ROUT. Inputs to INFIL include hourly precipitation,
daily temperature, and various trench cap characteristics.
IRRIG, IRRIGA - Foods may be irrigated with contaminated water from
either surface or groundwater sources. Input to IRRIG, which is called
only once per simulation, includes the time-averaged radionuclide
concentrations in well or surface water calculated by VERHOR or subroutine
SURSOL, respectively. IRRIG calls the function COV and uses the equations
in AIRDOS-EPA (Moo79, FiSOb) to calculate the time-averaged concentration
of each radionuclide from direct deposition by irrigation and subsequent
root uptake in foodcrops. Subroutine IRRIGA is called from MAIN each
simulation year.
LEACH - Subroutine LEACH calculates the amount of each radionuclide
from the homogeneous trench contents that leaves the trench each year.
3-8
-------
Losses may be via transport through the trench bottom or by overflow from
the trench. There are five independent user-specified methods that may be
used to calculate these amounts: the option is chosen by specifying a
value from one through five for parameter LEAOPT. Table 2-2 lists the
calculational methods corresponding to values of LEAOPT. The total-contact
options, 1 and 3, assume that all of the trench contents have been in
contact with water during the previous year. The immersed-fraction
options, 2 and 4, assume that the wetted fraction of the waste equals the
ratio of maximum water level to the trench depth. The distribution
coefficient options, 1 and 2, utilize a K,j approach to calculate the
radionuclide concentrations released from the wastes to the water, while
options 3 and 4 use a solubility estimate rather than K
-------
ROUT This subroutine is called by INFIL.
SIGMAZ - This subroutine is called by both AIRTRM and DPLT to compute
the vertical atmospheric dispersion parameters. Depending on the choice of
parameterization specified in the input data set, SIGMAZ will calculate the
dispersion parameters by one of eight schemes. Necessary input data
include the downwind distance, stability class, Hosker roughness parameter,
and lid height. Other data necessary for Lagrangian interpolations (by
function YLAG) are contained internally in SIZMAZ and need not be input by
the user.
SIMPUN - This subroutine, originally written by Banish (Bar70), uses
Simpson's rule to integrate along the ground level centerline of the
atmospheric plume to compute the depletion fraction. All input to SIMPUN
is supplied by DPLT, the subroutine that calls SIMPUN and to which the
results are returned.
SOIL - This is a subroutine called by ROUT.
SOURCE - Subroutine SOURCE reads the input required to initialize and
quantify transport parameters, except those required for subroutine INFIL.
Data concerning program control, climatic description, trench description,
aquifer description, atmospheric description, site-surface description, and
radionuclide description are read in by SOURCE. SOURCE also prints out
these data before any calculated results are output.
SURSOL - Subroutine SURSOL computes the amount of soluble radionuclide
that enters the stream annually. Input variables to SURSOL include the
3-10
-------
average depth of active exchange in the soil, the average downslope
distance to the stream, the cross slope extent of the spillage, the average
annual infiltration, the bulk density of soil, the amount of spillage, and
the surface soil distribution coefficients. Variables output from SURSOL
include the amounts of radionuclide going to the stream and the deep soil
layers and the radionuclide concentration in the interstitial water of the
contaminated surface region.
SUSPND - This subroutine calculates the above trench atmospheric
source term from the ground surface by two methods, a time-dependent
resuspension factor and a resuspension rate due to mechanical disturbance.
Input variables include the current year of simulation, the spatial area of
the contaminated surface, the radionuclide concentration on the ground
surface, the beginning and ending years of mechanical disturbances, the
resuspension rate, and the wind velocity. SUSPND assumes that all
radionuclides to be resuspended are deposited on the soil surface at a
simulation time zero. The resuspension factor calculated uses the
empirical equation of Anspaugh et al. (An75).
The atmospheric source term is returned to MAIN and is used along with
X/Q to calculate the air concentration of each radionuclide available for
deposition onto foodstuffs and for inhalation by the general population.
The value of X/Q is calculated by AIRTRM.
TRENCH - This subroutine determines the trench water balance. Input
variables include trench dimensions, porosity and permeability of trench
contents, trench water volume from the previous year, length of the
saturated zone, and annual precipitation and infiltration. Output from
3-11
-------
TRENCH includes the maximum depth of water in the trench, the volume of
water in the trench, volume of water overflowing the trench, and water
volume lost from the bottom of the trench.
The amount of water which overflows the trench, is calculated by
comparing the maximum water depth to the trench depth and overflowing any
amount greater than the trench volume. The variables VOLO, VOLB, OLDWAT,
and DMAX that quantify overflow, bottom loss, water level during previous
year, and maximum water depth in trench, respectively, are used by the
subroutine LEACH, discussed previously.
VERHOR - This subroutine calculates and decays the amount of each
radionuclide, that reaches the irrigation/drinking water well in a given
year. Variables evaluated elsewhere in the code and input to VERHOR
include the current year of the simulation, transit time from the trench to
the well, the volume of water leaving the trench bottom, the amount of each
radionuclide leaving the bottom of the trench, the amount of radionuclide
reaching the aquifer from the contaminated surface region, and the
radioactive decay constant.
YLAG - This function performs a Langragian interpolation as part of
the atmospheric transport calculations. The original program was written
by Brooks and Long (Br70) and adapted for use here. All input data are
supplied by subroutine SIGMAZ.
XPRESS - This subroutine computes and stores exponential decay factors
to be used repetitively in the nuclide loops. XPRESS saves a substantial
amount of computing time.
3-12
-------
4. DESCRIPTION OF OUTPUT OF THE PRESTO-EPA-POP CODE
The output of the PRESTO-EPA-POP code is designed to be self-explanatory
and provide descriptive comments, definitions, and intermediate tabulations
for a comprehensive description of the model simulation. The output from
PRESTO-EPA-POP is described in the following sections which correspond to
the output sections contained in the printout for a run. Full details on
operation of the PRESTO-EPA-POP code together with sample problem runs and
a source code listing are given in the PRESTO-EPA-POP Users Manual
(EPA85b).
4.1 REPLICATION OF INPUT DATA
The first section of the code output prints all input data, with the
exception of the input data for the subroutine, INFIL. Input data are read
and then written on a temporary storage device and then on the output
device. This record of the input data set is printed out for reference
identification of the run and verification of the input data. Input data
is subsequently read from the temporary storage device for use by the code.
INFIL input data is treated separately as shown in Section 4.4. This
approach preserves the modularity of the INFIL subroutine.
4.2 ORGANIZATION OF INPUT DATA
In the second section of the output of the PRESTO-EPA-POP code, the
input data are organized and summarized according to data type and transport
subsystem or pathway and then printed out. A detailed description of the
4-1
-------
input data together with sample computer runs can be found in the
PRESTO-EPA-POP User's Manual (EPA85b).
The first part of this output section consists of the computer run
identification and the user-supplied identification from the first input
card. The control information output identifies the site and interprets
the run control data entered. These control data include radionuclide
leaching options, trench cap failure data, and water use parameters. The
trench information output describes the trench area and depth, the porosity
of the trench contents, and the annual infiltration for the watershed.
The aquifer information output defines the groundwater velocity, the
trench to aquifer distance, the trench to well distance, the aquifer
thickness and contamination plume dispersion angle, the porosities of the
sub-trench area and the aquifer, the sub-trench permeability.
The atmospheric information output describes the effective source
height for the wind-blown mechanically mobilized contamination plume from
the site, the gravitational fall velocity of suspended soil particles, the
site-to-population distance, the lid height, the Hosker surface roughness
factor, the atmospheric stability class and dispersion formulation, the
fraction of the time wind blows toward the population, and the parameters
specifying the resuspension factor and resuspension rate.
The surface information output consists of the universal soil loss
equation parameters, the surface soil porosity and bulk density, the runoff
fraction for rainfall, the stream or river flow rate, the cross-slope extent
of spillage, the active soil depth, and the average distance from the
trench to the stream. The air and food chain information output describes
4-2
-------
productivity data for grass and vegetation, timing data for computation of
radioactive decay for the ingestion exposure pathway, and nuclide weathering
and carbon-14 equilibrium data. The water-food-chain output describes data
which characterize water use by milk cattle, goats, and beef cattle and
water use for crop irrigation.
Finally, the human ingestion and inhalation rate information is
printed.
4.3 RADIONUCLIDE SUMMARY TABLES
A set of three tables under the nuclide information heading summarizes
radionuclide data used for the transport calculations. First, an inventory
table specifies the initial inventory in the trench, on the soil surface,
in the stream, and in the atmosphere. Included in this table are
radioactive decay constants and the solubility constants. The second
table summarizes the chemical distribution coefficients for the surface
soil, the trench contents, the vertical soil column, and the aquifer. The
third radionuclide table summarizes the seven radionuclide-specific food
chain parameters used by the FOOD, IRRIG, HUMEX, CV, and COV subroutines.
These parameters are also used by the FOODA, IRRIGA, HUMEXA, CVA, and COVA
subroutines. Radionuclide atomic mass numbers are extracted from the
radionuclide names and used in the calculations. Results from the mass
extraction algorithm are printed in the initial calculations table.
4-3
-------
4.4 INFIL INPUT/OUTPUT
The fourth section 'of output of the code consists of the input data
and results produced by the subroutine INFIL. INFIL control data are given,
followed by monthly average values for hours of sunshine, daily average
temperature levels, and hourly rainfall amounts.
The trench characteristics presented are the snowmelt coefficient,
trench cover thickness, width, slope, permeability, porosity for gravity
and pellicular water, equivalent upward diffusivity, and equivalent upward
hydraulic conductivity. The INFIL time step is also printed. Results are
annual precipitation, evaporation, runoff, and cap infiltration.
4.5 UNIT RESPONSE CALCULATIONS
This output section includes results of nuclide-specific annual trans-
port calculations which will be used by the bookkeeping submodels for each
simulation year. The outputs also includes soil loss calculation results
and the calculated or input value for the ratio of atmospheric radionuclide
concentration per unit release rate at the radionuclide disposal site.
4.6 ANNUAL SUMMARY TABLES FOR SPECIFIED YEARS
Control variables determine the years for which results will be given.
For those years, a number of hydrologic and transport variables are output.
Included are trench cap status, maximum possible water depth in the trench,
water loss by overflow and drainage from the trench, and trench inventory.
Radionuclide concentration values and flux values are presented for key
pathways and regions of interest.
4-4
-------
4.7 RADIONUCLIDE CONCENTRATION TABLES
The radionuclide concentration tables present, by nuclide, the average
concentration over the entire assessment period, the year of maximum
concentration, and the maximum concentrations for the atmosphere, well
water, and stream water. Because human exposures may commence and peak
many years after closure of a disposal site, the year and level of maximum
concentration are important since they are related to the year at which
population exposures are most significant.
Separate average radionuclide concentration tables for the user-
specified averaging time period are included. These tables present the
radionuclide concentration in five types of foods resulting from
atmospheric nuclide deposition and irrigation.
4.8 RADIONUCLIDE EXPOSURE TABLES
Annual population intakes of radionuclides by ingestion and by
inhalation are output and the fraction of ingestion dose from drinking
water is given. The radionuclide exposure tables list by nuclide the year
of maximum exposure and the corresponding level of the maximum, mean
population exposure from the atmosphere, the ground surface and for
ingestion and for inhalation. Although the exposure terms are dependent on
the concentrations summarized in the concentration tables, the times of
maximum exposures will in general differ from the times of maximum
concentrations. This difference occurs because of the dependence of
4-5
-------
exposure on soil concentration and the nuclide-specific uptake and
concentration mechanism of the food chain which are considered in computing
exposures from ingestion.
4.9 DARTAB CONTROL INFORMATION
DARTAB control information includes run identification data, summaries
of output table control information, lists of critical organs and cancers
to be considered in the run, dose equivalent factors for low and high
linear energy transfer (LET) radiation, radionuclide uptake and clearance
data, and lists of nuclides and organ dose or cancer risk factors not found
in the RADRISK data sets which were accessed by DARTAB. The location of
the population at risk, the lifetime fatal cancer risk at that location,
and the organ dose weighting factors are also given.
4.10 DARTAB DOSE TABLES
DARTAB dose tables are produced in the code output and present
individual and collective dose summary rates by low and high LET radiation
and organ, by low and high LET radiation and exposure pathway, and by low
and high LET radiation and radionuclide. Both absolute dose and percentage
of total dose are included in these tables.
4.11 DARTAB FATAL CANCER RISK TABLES
DARTAB fatal cancer risk tables produced in the output present
individual and collective fatal cancer risk, premature death, and lifetime
4-6
-------
fatal cancer risk exposure equivalent. Genetic risks are also summarized.
Values are summarized by low and high LET radiation, by organ, and also by
pathway.
4.12 RESIDUAL RADIOACTIVITY RELEASED TO THE BASIN AND HEALTH EFFECTS
This output section gives that amount of radionuclides released to the
basin each millenium during the 10,000 year simulation. The aggregated
total release of each radionuclide, the health effect conversion factor,
and the basin population health effects by radionuclide are given.
4-7
-------
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APPENDIX A
A MODEL TO SIMULATE INFILTRATION OF RAINWATER
THROUGH THE COVER OF A RADIOACTIVE WASTE TRENCH
UNDER SATURATED AND UNSATURATED CONDITIONS
-------
APPENDIX A
This appendix contains the background theory of the infiltration
submodel (subroutine INFIL) used in PRESTO-EPA-POP as developed by Hung
(Hu83). Hung's analysis follows.
A MODEL TO SIMULATE INFILTRATION OF RAINWATER
THROUGH THE COVER OF A RADIOACTIVE WASTE TRENCH
UNDER SATURATED AND UNSATURATED CONDITIONS
INTRODUCTION
The disposal of low-level radioactive wastes by the shallow land
burial method has been used for decades. An important consideration in
evaluating the performance of a waste disposal site is the potential
effects on the health of nearby populations. Since one of the major
driving forces in causing the release of radionuclides is the rainwater
which infiltrates through the cover of a disposal trench, simulating the
infiltration process is an important part of any model for evaluating
health effects.
An accurate model for simulating the infiltration of rainwater through
a trench cover involves the modeling of three flow systems: an overland
flow system, a subsurface flow system, and an atmospheric diffusion system.
The overland flow system receives the rainwater and diverts the excess
water from percolation and evaporation into the receiving drainage system.
The subsurface flow system receives the percolated water from the overland
flow system and transports the water either downward as infiltration into
the trench and/or upward as evaporation into the atmospheric diffusion
system. The atmospheric diffusion systems receives water/vapor from the
overland flow system or subsurface flow system and transports the vapor to
A-2
-------
the atmosphere. One of the early efforts in simulating this system for
storm runoff was the Stanford Watershed Model conceived by Crawford and
Linsley (O66). The same model was significantly improved by Moore and
and Claborn (Mo71) and Hung and Keifer (Hu77). However, these models were
developed for water resources planning purposes with emphasis on the
overland flow system. Significant improvements are required to apply the
same models to the simulation of trench cover infiltration. This study
presents an efficient and yet accurate infiltration model based on the
dynamic equations governing the above systems.
BASIC EQUATIONS
The simulation of rainwater movement through a homogeneous trench
cover, defined here as the "total infiltration system," involves analyzing
the hydrologic processes of overland flow, subsurface flow, and atmospheric
diffusion systems. The basic momentum and continuity equations governing
these three systems have been studied thoroughly by other investigators.
They are discussed below.
Overland Flow System - The one-dimensional momentum and continuity
equations governing an overland flow system are expressed by (Iw64),
and
8h 9u ah
+ h + U = P ' E°
where
u = velocity of overland flow
h = depth of flow
A-3
-------
a = average inclination of the trench cover
n = Manning's coefficient of roughness
P = rate of precipitation
E0 = rate of evaporation from the overland flow
q0 = rate of percolation from the overland flow system
g = acceleration potential due to gravitational force
x = space coordinate along the slope of the trench cover
t = time
The above equation is derived from the assumptions that Corioli's energy
correction factor, Boussinesq's momentum correction factor, and Jaeger's
hydrostatic pressure correction factor are all unity;; the flow is one
dimensional, i.e., the velocity component in the longitudinal direction
predominates the velocity component in lateral directions, and the flow is
a gradually varied flow. The above system equations cannot be solved
independently and must be coupled with the basic equations governing the
other two systems.
Because Manning's law of resistance is an empirical formula developed
for open-channel flow, it is conceivable that the application of the same
law to a thin overland flow may be questionable. However, comprehensive
laboratory and field studies conducted by Takasao and Kishimoto (Ta61) and
Ishihara and Takasao (Is62,Is63) indicated that the Manning Law can also
reasonably be applied to an overland flow system. This finding was
confirmed by Foster, Huggins, and Meyer (Fo68) and Hjemlfelt (Hj81).
A-4
-------
Subsurface Flow System - The movement of soil moisture in a subsurface
flow system can be either upward or downward depending on the direction of
the potential head gradient. In general, the moisture in the soil is
simultaneously transported in both liquid and vapor phases. The basic
equation governing this system has been derived by Currie (Cu61) and Hi 11 el
(Hi80). The results of their studies for the momentum and continuity
equations are summarized as follows
q = _DL (W)+ K(W) - bD - (A-3)
9z 9z
and
aw
- <*-<>
where
q = flux of moisture in the vertical direction
W = volumetric wetness of soil
K = hydraulic conductivity
D|_ = hydraulic diffusivity
b = conversion factor for transforming the vapor flux into liquid
water flux
D = diffusivity for water vapor
C = concentration of water vapor in the air-filled void
The above equations were based on an isothermal condition and assumed that
both viscous flow in the liquid phase and diffusion of vapor are impelled
by the force field of capillarity and gravity. No explicit account has
been taken of osmotic or solute effects on vapor pressure. In reality, the
upper layer of the soil surface is warmer during the daytime and cooler
A-5
-------
than the deeper layer during night time. The movement of vapor due to the
thermal gradient effect tends to be downward during the day and upward
during the night. Therefore, the error due to the assumption that the
system is isothermal may compensate each other within the same day and will
not significantly affect the accuracy of simulation.
Atmospheric Diffusion System - The atmospheric diffusion system
transports the water vapor through the turbulent boundary layer into the
atmosphere. The vapor transport through an unsteady turbulent boundary layer
involves the analysis of the time-averaged boundary layer equations for the
air stream and the continuity equation for the water vapor. This analysis
is extremely complicated. However, by assuming the system is quasi-steady,
the solution of the system equation is obtainable. The "quasi-steady"
technique has been commonly used in solving unsteady mass transport systems.
It assumes that within a small time increment the flow of the carrying fluid
is steady and that the effect of the change from one flow state to the other
due to the change in time step is negligible. By imposing the above assump-
tion, the water vapor flux within the fully developed boundary layer was
expressed by employing Pick's law for diffusion (Bi66) as
j = _k2y2 ^/ dCb (A_5)
where
J = water vapor flux
k = Prandtl's mixing length coefficient
v = time overaged wind speed
C^ = concentration of water vapor in the boundary layer
y = distance from ground surface
A-6
-------
BASIC EQUATIONS FOR THE PRACTICAL METHOD
Theoretically, the basic equations compiled in the previous section
can be solved numerically. However, the processes of analysis are
complicated and consume excessive computation time. Several attempts have
been made to solve a simplified system. For example, a conjunctive
overland-subsurface flow model without atmospheric diffusion system has
been developed by Akan and Yen (Ak81), and a subsurface flow-atmospheric
diffusion model without overland flow system was reported by Hi 11 el and van
Bavel (Hi76a) and Hillel (Hi76b). The above models solve the dependent
variables as functions of space and time and involve long and costly
calculations if the real time of simulation is prolonged. For example, the
time increment used in Akan and Yen's overland flow system was 30 seconds
which would require excessive computation costs if the simulation were for
a year or more.
One may simplify the above system equations by transforming all of the
space-dependent variables into space-independent variables to avoid
time-consuming simulation. The transformation for each system is described
in the following sections.
Atmospheric Diffusion System - The solution of Equation (A-5) depends
on many complicated fluid dynamic and boundary conditions. One of the
simplest solutions is obtained by assuming that the vapor flux will not be
limited by the availability of vapor transmitted from the subsurface system
or the overland flow system. The vapor flux under this condition is known
as the evaporation potential and is normally used as the upper bound of the
evaporation rate from the overland flow and subsurface flow systems. The
actual evaporation rate from these systems may then be calculated from the
A-7
-------
conjunctive system to be discussed later. The solution of Equation (A-6)
under the above condition was proposed by Rohwer (Ro31) as
Ep = 0.372(1-0.000374pa)(l. + 0.6Vw)(es - ea) (A-6)
where
Ep = evaporation potential
pa = atmospheric pressure
Vw = wind speed
es = saturated vapor pressure
ea = vapor pressure in the atmosphere
Equation (A-6) requires time-dependent input for atmospheric pressure,
wind velocity, and vapor pressure to compute the diurnal variation of
evaporation potential. The above information is normally not readily
available from existing records. Therefore, from a practical viewpoint,
the computation of evaporation potential may be reduced to a daily average
level by using the Hamon Equation (Ha61)
Ep = Nr2s (A-7)
where
N = coefficient of daily evaporation potential
r = duration of daylight in 12-hour unit/day
s = saturated absolute humidity corresponding to the daily average
temperature
Equation (A-7) is used to calculate the evaporation potential which is the
upper bound of the evaporation rate.
A-8
-------
Overland Flow System - It is well known that the local and convective
acceleration terms in Equation (A-l) govern the wave form and the celerity
of flood waves. Kicftikawa (Ki59) indicated that these terms are
predominated by the friction term and suggested that they may be ignored.
This conclusion was also confirmed by Takasao and Kishimoto (Ta61) and
Ishihara and Takasao (Is62) of overland flow systems through laboratory and
field observations. Takasao further simplified the system equations by
replacing the space dependent depth of flow h by an average flow depth.
After this modification, Equations (A-l) and (A-2) become
and
Qo =
H5/3
(A-8)
_ Qo
(A-9)
where
Q0 = rate of overland flow per unit width of trench cover
H = average depth of overland flow over the entire trench cover
L = length of slope (or half of trench width)
Furthermore, it is assumed that the rate of evaporation from the total
infiltration system will be preferentially obtained from the overland flow
system, then the component of evaporation rate may be written as
H
ED when P + > ED
K At v
P + when Ep > P + > 0
\f
At
(A-10)
0 when P + = 0
At
A-9
-------
where
E0 = component of evaporation rate contributed by the overland flow
system
On the other hand, since the maximum rate of percolation from the
overland flow system cannot exceed the saturated hydraulic conductivity of
the trench cap, the percolation rate can be written as
Ks when P - E0 + > Ks
At
q0
P - E0 +JL when Ks > P - E0 + JL > 0 (A-ll)
0 when P - E0 + - = 0
The above expressions show that there are four equations available for
solving the four dependent variables, Q0, H, E0, and q0. Therefore, the
system can be solved independently.
Subsurface Flow System - For the purpose of transforming the space
dependent variables into space independent variables, the moisture contained
in the system may be divded into three components: gravity, pellicular,
and hygroscopic waters. Gravity water is the moisture in a soil which can
be drained by gravity force; pellicular water is the moisture in a soil
which cannot be drained by gravity force but can be lost to the atmosphere
through natural evaporation; and hygroscopic water is the moisture which
will never be lost through the above natural processes. Furthermore, it is
assumed that soil wetness can be mathematically approximated by a step-wise
distribution composed of these three components. Figure A-l shows a
comparison of the step-wise wetness distribution and its corresponding
original wetness distribution.
A- 10
-------
WETNESS
TOP OF TRENCH CAP
GRAVITY WATER DEFICIT
PELLICULAR WATER DEFICIT
STEP-WISE WETNESS
DISTRIBUTION CURVE
BOTTOM OF TRENCH CAP
^ -^^
COMPONENT
FOR HYGROSCOPIC WATER
COMPONENT
FOR GRAVITY WATER
COMPONENT OF POROSITY
FOR PELLICULAR WATER
RAE-102213
FIGURE A-l. COMPARISON OF A SCHEMATIC NATURAL WETNESS DISTRIBUTION
CURVE AND ITS CORRESPONDING STEP-WISE WETNESS DISTRI-
BUTION CURVE.
A-ll
-------
Based on the above concept, the dependent variables appearing in the
basic differential equations may be divided into three components, i.e.,
VI = Wi + W2 + W3
and q = qi +
where
W^ = component of wetness for the hygroscopic water
W2 = component of wetness for the pellicular water
W3 - component of wetness for the gravity water
q^ = component of flux for the hygroscopic water
q2 = component of flux for the pellicular water
q3 = component of flux for the gravity water
qt = flux of moisture being transformed from gravity water to
pel 1 icul ar water
Substituting Equation (A-12) into Equations (A-3) and (A-4) gives
q3 = -DL(W)3 + K(W)
9 z
K(W) = 0, when W3 = 0
and _M3 . . 8(q3-
at az
for the component of gravity water and
q2 = -DL(W)_ + K(w) _ bD
az az '
K(W) > 0 when W3 > 0
and aW2 = _
ot
for the component of pellicular water.
A-12
-------
Applying the step-wise wetness distribution concept to the above system
equations, Equations (A-13) and (A-14) may be rewritten by substituting the
proper difference forms of the dependent variables. The result is
0 when Zg = Zmax
and tla
^- - (qi -%
where
q-j = flux of moisture infiltrating into the trench
Ks = saturated hydraulic conductivity of the soil
Zg = deficit of gravity water
^max = maximum of deficit of gravity water (equivalent to the
thickness of the trench cover)
Wq = component of wetness for the gravity water under a fully
saturated conditions and is numerically identical to the
porosity for the gravity water
To simplify the solution of Equation (A-15), the component of moisture
flux for the pellicular water, q2» is computed based on the assumptions
that (1) the flow is predominated by liquid phase transport or (2) the flow
is predominated by vapor phase transport. The moisture flux for the
pellicular water at any instant is then chosen from, the larger flux
calculated from the above two assumptions.
When the flow is predominated by a liquid phase transport, the third
term in Equation (A-15) vanishes. Substituting the proper difference form
of the dependent variables gives
A-13
-------
qL = -DeWp/Zp + Ke
and - qL < Ep - E0
where
qi_ = flux of pellicular water transported in the liquid phase
Wp = component of wetness for the pellicular water under fully
saturated condition and is numerically identical to the
porosity for pellicular water
Zp = deficit of the pellicular water
De = hydraulic diffusivity at equivalent wetness
Ke = hydraulic conductivity at equivalent wetness
The equivalent wetness for the purpose of this study is calculated by
We = Wh + SWp (A-20)
where
W^ = component of wetness for the hygroscopic water under fully
saturated condition and is numerically identical to the
porosity for hygroscopic water
S = coefficient of equivalent wetness for pellicular water which
should be greater than 0.5 and smaller than 1.0
When the flow is predominated by vapor phase transport, the first and
second terms on the righthand side of Equation (A-15) disappear. Substitut-
ing the proper difference form of the dependent variables, Equation (A-15)
becomes
qv = -bDv(Cs - C0)/Zp (A-21)
A-14
-------
where
qv = flux of moisture being transported in the vapor phase
Dv = diffusivity of water vapor in the trench cap
Zp = deficit of pellicular water
Cs = water vapor concentration at the front of pellicular water
C0 = water vapor concentrations at the top of trench cover
The diffusion of water vapor from the top of the trench cover to the
atmosphere can be written based on Pick's Law as
qv = -bDa(co - Ca)/Tb (A-22)
where
i
qv = flux of water vapor in the boundary layer of diffusion
Da = diffusivity of vapor in the boundary layer
TI-, = equivalent thickness of boundary layer
Ca = water vapor concentration in the atmosphere outside the
boundary layer
Since the vapor flux in the trench cover and in the boundary layer
should be identical, Equations (A-21) and (A-22) may be combined to yield
= . bDa(cs - Co)/Tb
1 + a
(A-23)
TbDv
Furthermore, the ratio of diffusivities, Da/Dv, may be obtained from
Penman's (Pe40) study on the diffusion of vapor through a porous solid and
Rohwer's (Ro31) study on evaporation potentials. Substituting their
results into Equation (A-23) and replacing the numerator with the
evaporation potential yields
A-15
-------
1 + 0.6V Z (A_24)
T^0.66(Wp + Wg)
For the purpose of this study, the coefficient, (l+O.eVy)/!^, is
assumed to be a constant and equal to 0.5m~^ (see section on Model
Testing). When this coefficient is used, Equation (A-24) becomes
0.66(Wp + Wg)
(A-25)
Now, the flux of moisture being lost through evaporation qp can be
computed by
qp = -Max( | qL , | qv | ) (A-26)
where the Max function implies the selection of the largest number among
those values designated in the parentheses.
Again, by substituting the proper difference form of the dependent
variables, Equation (A-16) becomes
dZp/dt = -(qp + qt)/Wp (A-27)
where q^ may be computed by
' q0 when Zp > 0
0 when Zp = 0
(A-28)
Equations (A-8 through A-10), (A-ll), (A-17 through A-19), and (A-25
through A-28) are the basic equations for the practical infiltration model.
There are eleven equations and eleven dependent variables in the system
A-16
-------
equations. Since all of the dependent variables are space independent and
each pair of momentum and continuity equations can be solved in sequence,
the computer coding for the mathematical model is greatly simplified from
that of the original system equations. A computer model has been developed
for testing the proposed system equations and for the application of the
model to the evaluation of a low-level waste disposal site.
MODEL TESTING
The overland flow system using Equations (A-8) and (A-9) as basic
equations, has been studied through laboratory studies and field observa-
tions by Takasao (Ta61). They concluded that the space independent system
equations, as represented by Equations (A-8) and (A-9), can reasonably be
used to characterize the nature of overland flow for flood routing
purposes. Since the primary purpose of this study is the simulation of
infiltration rates, the proposed overland flow system equations are judged
to be adequate for the infiltration model. Testing of the model was
therefore concentrated on the subsurface flow system. To test the
subsurface flow system submodel, three special cases with simplified
boundary conditions were selected. The results of simulation were compared
with existing studies having the similar boundary conditions. They are
described in the following sections.
Gravity Water Drainage Without Evaporation - A computer simulation of
gravity water drainage by gravitational force without evaporation loss was
conducted by Hillel and van Bavel (Hi76a). This simulation was conducted by
solving equations similar to the basic differential equations expressed in
Equations (A-3) and (A-4) without the term representing the vapor phase
transport. The results of simulation for a sandy soil (1.16 m thick) were
A-17
-------
used to calculate the cumulative water volume being drained from the soil
(see Figure A-2).
By applying the same boundary conditions used in Hi lie! and van
Bavel's study to the model developed for this study, the cumulative water
volume drained from the soil is simulated and plotted in Figure A-2. The
comparison of the two results indicates that the proposed model does not
simulate the time variation of the drainage precisely, but the calculation
of the cumulative water volume drained from the soil is reasonably close to
the results obtained from Hillel and van Bavel's simulation. Since the
main purpose of the simulation described in this study is to obtain the
cumulative volume of water infiltrated into the waste trench, the proposed
model simulates the rate of infiltration with acceptable accuracy.
Steady State Evaporation Rate - The steady state evaporation rate from
a clay soil system with a relatively high groundwater table has been
analyzed by Ripple (Ri72). This study analyzed the evaporation rate by
solving the system equation characterizing the water flux transported in
the subsurface flow system and the vapor flux diffused into the atmosphere.
The results of his analysis for the groundwater table at depths of 0.6,
0.9, 1.2, and 1.8 meters are shown in Figure A-3.
By applying similar parameters and boundary conditions to the proposed
model and reorganizing the results into the form corresponding to Ripple's
results, the results as shown in Figure A-3. The results of simulation
from the proposed model fit reasonably well with those obtained by Ripple.
The above evaporation rate was simulated for a relatively shallow
groundwater table. Therefore, the transport of soil moisture is dominated
A-18
-------
^RESULTS OBTAINED FROM THIS STUDY
RESULTS INTERPRETED FROM HILLEL AND VAN BAVEL'S STUDY
345
TIME IN DAYS
8
RAE-1020125
FIGURE A-2. COMPARISON OF THE RESULTS OF SIMULATIONS FOR GRAVITY DRAINAGE
OF A TYPICAL SAND USING THE PROPOSED MODEL AND RESULTS
INTERPRETED FROM HILLEL AND VAN BAVEL's STUDY.
-------
1.00
ro
o
DEPTH=60 cm
DEPTH = 90 cm
DEPTH =120 cm
DEPTH =180 cm
RESULTS OBTAINED BY RIPPLE
-' RESULTS OBTAINED BY THIS STUDY
.1 .2 .3 .4 .5 .6
EVAPORATION POTENTIAL (cm/day)
RAE-102209
FIGURE A-3. COMPARISON OF THE RESULTS OF SIMULATION FOR THE STEADY STATE
EVAPORATION OF CHINO CLAY BY USING THE PROPOSED MODEL AND THAT
OBTAINED BY RIPPLE.
-------
by liquid phase transport. However, when the groundwater table is very
deep, the steady state rate of evaporation may be dominated by the vapor
phase transport. The computation of vapor transport in Equation (A-25)
becomes important under this condition.
Vapor Phase Transport - There are no data available for evaluating the
transport of pellicular water in a vapor phase. To compare the character-
istics of vapor phase transport and liquid phase transport, the flux of
moisture being transported by these two phases are computed for various
depths of pellicular water deficit based on Equations (A-19), (A-25), and
(A-26), using evaporation potentials of 0.3 and 0.6 cm/d. The results of
analysis for both sandy and clay soils are plotted and presented in
Figure A-4. The coefficient represented by (l.+0.6Vw)/T|j as 0.5m"-'- was
selected to obtain the best transition from liquid phase transport to vapor
phase transport for both soils and for the evaporation potentials which
ranged from 0.3 to 0.6 cm/d. The trend of pellicular water flux variations
with the increase in the pellicular water deficit agrees, in general, with
the trend described by Philip (Ph74).
APPLICATION OF MODEL TO AN ACTUAL WASTE DISPOSAL SITE
The low-level radioactive waste disposal site located at Barnwell,
South Carolina, was selected for an application of the model to an actual
waste disposal site. The trench cover is constructed in two soil layers,
loamy sand (120 cm thick) at the top and clay soil (80 cm thick) at the
bottom. First, the analysis simulated the infiltration rates for a
homogeneous trench cover for each of the soil types constituting the trench
cover; then, the rate of infiltration for the composite trench section was
interpreted from the results.
A-21
-------
SANDY SOIL
EVAPORATION POTENTIAL = 0.6 cm/day
EVAPORATION POTENTIAL = 0.3 cm/day
EVAPORATION RATE USED IN THE MODEL
EVAPORATION RATE TRANSPORTED IN LK3UD PHASE
EVAPORATION RATE TRANSPORTED IN VAPOR PHASE
i I I i
.2 .3 .4 .5
RATE OF EVAPORATION (cm/day)
= ~ 1
O
sg
I
<
CLAY SOIL
7
EVAPORATION POTENTIAL = 0.6 cm/day
EVAPORATION POTENTIAL = 0.3 cm/day
EVAPORATION RATE USED IN THE MODEL
EVAPORATION RATE TRANSPORTED IN UQUD PHASE
EVAPORATION RATE TRANSPORTED IN VAPOR PHASE
I i I i
.2
.3
.4
.5
.6
RATE OF EVAPORATION (cm/day)
RAE-102124
FIGURE A-4. TRANSITION IN PELLICULAR WATER TRANSPORT FROM
LIQUID PHASE TO VAPOR PHASE CALCULATED FROM
EQNS. A.19, A.25, AND A.26 FOR SANDY AND
CLAY SOILS.
A-22
-------
The soil characteristics for both layers were interpreted from basic
data reported by Chem-Nuclear Systems, Inc. (CNS80), and the results used
for the computer simulation are listed in Table A-l.
Using the annual rainfall of 118 cm/yr and the rainfall distribution
pattern observed in Augusta, Georgia, the simulation was conducted for the
loamy sand and the clay soil. The results of simulation, presented in
Figure A-5, indicate that the infiltration rates are 45 cm/yr for the loamy
sand and 7 cm/yr for the clay soil. It is obvious that the rate of
infiltration will not be affected by the soil characteristics below the
level of annual maximum deficit for pellicular water plus the allowance for
gravity water storage. The pellicular water deficit simulated for the
loamy sand (Figure A-6) indicated that the maximum pellicular water deficit
reached the level of approximately 50 cm which is far above the upper
boundary of the clay soil layer (120 cm below the top of trench cap).
Thus, one may conclude that the infiltration rate for the Barnwell site is
controlled by characteristics of the top layer, and the rate of
infiltration is 45 cm/yr or 17.7 in/yr.
The above analyses assumed a uniform rainfall distribution within the
hourly period when the rainfall was recorded. However, the rainfall
distribution within any hour in a real case is not necessarily uniform. By
assuming a peak factor of two, i.e., all of the rainfall being recorded
hourly is assumed to be concentrated in the second half of the recorded
period, and reapplying the same input data to the infiltration model to
rerun the case for the loamy sand (top layer), the rate of infiltration is
35 cm/yr or 13.8 in/yr. Therefore, the infiltration rate for the Barnwell
site may vary between 13.8 and 17.7 in/yr due to the nonuniform hourly
rainfall distribution.
A-23
-------
TABLE A-l
SOIL CHARACTERISTICS OF THE TRENCH COVER USED IN
SIMULATING THE ANNUAL RAINFALL INFILTRATION,
BARNWELL, RADIOACTIVE WASTE DISPOSAL SITE
ro
Type
Top Layer
Loamy Sand
Saturated
Hydraulic
Conductivity
(m/hr)
0.02
Equivalent
Upward
Diffusivity
(m2/hr)
0.02xlO-2
Equivalent
Upward
Conductivity
(m/hr)
0. 12xlO-5
Porosity
Total
0.51
Porosity
Pellicular
Water
0.24
Porosity
Gravity
Water
0.25
Bottom Layer
Clay Soil
0.005
0.13x10
-3
O.OlxlO-4 0.54
0.44
0.08
-------
. o 150
100
50
ui
LOAMY SAND (Top Layer)
TOP LAYER: LOAMY SAND, kma =2.0 cm/hr
max
567
TIME (Months)
8 9 10 11 12
150
Bfz
o o
il
-fjj 100
DC
UJ
50
CLAY (Bottom Layer)
BOTTOM LAYER: CLAY. kmax = 0.5 cm/hr
> °
LU 0
4567
TIME (Months)
8 9 10 11 12
RAE-102121
FIGURE A-5. THE RESULTS OF SIMULATIONS USING THE PROPOSED MODEL FOR
LOAMY SAND AND CLAY SOIL, BARNWELL, S.C., RADIOACTIVE
WASTE DISPOSAL SITE.
A-25
-------
ro
01
E
o
^x
Sit
0
50
2 uj ioo
1KPI
O. LU 150
H
<
200
0
BOUNDARY OF TOP AND BOTTOM LAYERS
45678
TIME (months)
10 11 12
RAE-102210
FIGURE A-6. THE RESULTS OF SIMULATING THE VARIATION OF PELLICULAR WATER DEFICIT,
LOAMY SAND, BARNWELL, S.C. RADIOACTIVE WASTE DISPOSAL SITE.
-------
Independent studies have been conducted by the U.S. NRC (NRC82) and
the U.S. Geological Survey on the rate of infiltration for the Barnwell
site, based on an analysis of groundwater being discharged to a nearby
creek. NRC's analysis indicated a rate of 14 in/yr; USGS's, 14 to 17 in/yr.
The results of simulation using the infiltration model are in agreement
with these two studies.
CONCLUSIONS
1. The space-dependent variables in the momentum and continuity
equations of a subsurface flow system can be transformed into
space-independent variables by breaking down the soil moisture
into gravity water, pellicular water, and hygroscopic water
components.
2. The results of transformations for the overland flow system,
the subsurface flow system, and the atmospheric diffusion
system have greatly simplified the computational procedures
for simulating these systems and have improved the stability
and efficiency of the numerical analysis.
3. Although the transformed system equations cannot simulate the
dynamic response of soil moisture as precisely as the original
partial differential equations, the derived system equations
can be used to simulate the long-term infiltration rates with
reasonable accuracy.
4. When the model was applied to the Barnwell radioactive waste
disposal site, the results of simulation fit very well with
the results of analysis conducted by other investigators
A-27
-------
using the other methods. This fact implies that the proposed
model can be employed to simulate the infiltration of rain-
water through the cap of a waste disposal trench.
5. The proposed practical infiltration model is suitable for
integrating into a larger system model for risk assessment
of a low-level radioactive waste disposal site.
A-28
-------
APPENDIX A REFERENCES
Ak81 Akan, A. S. and B. C. Yen, "Mathematical Model of Shallow Water Flow
over Porous Media," J. of Hydr. Div., ASCE HY4, April 1981.
Bi66 Bird, R. B., W. E. Stewart and E. W. Lightfoot, Transport Phenomena,
Seventh Edition, John Wiley and Sons, Inc., New York, 1966.
Ca86 Cahill, J., "Movement of Radionuclides in Unconsolidated Burial Site
Near Barnwell, South Carolina," (in press).
CNS80 Chem-Nuclear Systems, Inc., Environmental Assessment for Barnwell
Low-Level Radioactive Waste Disposal Facility, Chem-Nuclear Systems,
Inc., Columbia, South Carolina, 1980.
Cr66 Crawford, N. H., and R. K. Linsley, Digital Simulation in Hydrology:
Stanford Watershed Model IV, Technical Report No. 39 (Department of
Civil Engineering, Stanford University, Stanford, California), 1966.
Cu61 Currie, J. A., "Gaseous Diffusion in Porous Media, Part 3 - Wet
Granular Material," Brit. J. Appl. Phys. 12, 275-281, 1966.
Fo68 Foster, G., L. Huggins, and L. Meyer, "Simulation of Overland Flow
on Short Field Plots," Water Resources Research, Vol. 4, No. 6,
1968.
Ha61 Hamon, W. R., "Estimating Potential Evapotranspiration," ASCE, HY3,
1961.
Hi76a Hillel, D. and C. Van Bavel, "Simulation of Profile Water Storage as
Related to Soil Hydraulic Properties," J. Soil Science Society of
America, Vol. 40, No. 6, November 1976.
Hi76b Hi lie!, D., "On the Role of Soil Moisture Hysteresis in the
Suspension of Evaporation from Bare Soil Under Diurnally Cyclic
Evaporativity," Soil Science, 122, 6, 1976.
Hi80 Hillel, D., Fundamentals of Soil Physics, pp. 221-223, Pergammon
Press, New York, 1980.
Hj81 Hjelmfelt, A., "Overland Flow Time Distributed Rainfall," Journal of
Hydraulic Division, ASCE, February 1981.
Hu77 Hung, C. Y. and C. J. Keifer, "Storm Runoff Simulation for the Lake
Diversion Area," a report prepared for the Illinois Department of
Transportation, Division of Water Resource, February 1977.
Hu83 Hung, C. Y., G. L. Meyer, and V. C. Rogers, Use of PRESTO-EPA Model
in Assessing Health Effects from Land Disposal of LLW to Support
EPA's Environmental Standards: U.S. Department of Energy, Proceed-
ings of 5th Annual Participants' Information Meeting on DOE Low-Level
Waste Management Program, Denver, Colorado, August 30, 1983,
CONF-8308106, Idaho Falls, Idaho.
A-29
-------
Is62 Ishihara, T. and T. Takasao, "A Study on the Subsurface Runoff and
Its Effects on Runoff Process," Trans JSCE No. 79, 1962.
Is63 Ishihara, T. and T. Takasao, "A Study on the Runoff Pattern and Its
Characteristics" Bull. Disaster Prev. Research Inst., Japan, No. 65,
1963.
Iw64 Iwasa, Y., "Fundamental Principles of Open-Channel Flow," published
by Hydraulic Committee, Japan Society of Civil Engineers, 1964.
Ki59 Kichikawa, H., "A Study on the Underground Flood Control Reservoir,"
Proceedings, JSCE, 1959.
Mo71 Moore, W. L. and B. J. Claborn, "Numerical Simulation of Watershed
Hydrology," in proceedings of the First Bilateral U.S.-Japan Seminar
in Hydrology, January 1971.
Pe40 Penman, H. L., "Gas and Vapor Movement in the Soil: I, the
Diffusion of Vapor Through Porous Solids," Journal, Agr. Sci., 30,
pp. 437-461, 1940.
Ph74 Philip, J. R., "Water Movement in Soil," pp. 29-47. Ed. D. A.
De Varies and N. H. Afgan, Halsted Press-Wiley, New York, 1974.
Ri72 Ripple, C. C., J. Rubin, and T. Van Hylkama, "Estimating Steady-State
Evaporation Rate from Bare Soil Under Conditions of High Water Table,"
U.S. Geological Survey, Water Supply, pp. 2019-A, 1972.
Ro31 Rohwer, C., "Evaporation from a Free Water Surface," U.S. Department
of Agriculture, Tech. Bull. 271, 1931.
Ta61 Takasao, T. and S. Kishimoto, "An Experimental Study on the Runoff
of Rainfall," Bull., Disaster Prev. Research Inst., Japan, No. 4,
1961.
NRC82 U.S. Nuclear Regulatory Commission, Environmental Assessment for the
Barnwell Low-Level Waste Disposal Facilities, NUREG-0879, Division
of Waste Management, 1982.
A-30
-------
APPENDIX B
AN OPTIMUM GROUNDWATER TRANSPORT MODEL FOR
APPLICATION TO THE ASSESSMENT OF HEALTH EFFECTS
DUE TO LAND DISPOSAL OF RADIOACTIVE WASTES
-------
APPENDIX B
This appendix presents background and theory for the groundwater
transport model and DDETA correction factor used by the MAIN routine and
VERHOR subroutine in the PRESTO-EPA-POP code. The model was developed by
Hung and the original publication is included here.
5-2
-------
NLCI.EAR ANDCHKMICAL WASTK MANACEMKST. Vol. 6, pp. 41-50, 1986
Printed m [he USA. All nghls reserved.
AN OPTIMUM GROUNDWATER TRANSPORT MODEL
FOR APPLICATION TO THE ASSESSMENT OF
HEALTH EFFECTS DUE TO LAND DISPOSAL
OF RADIOACTIVE WASTES
Cheng Y. Hung
Office of Radiation Programs, U.S. Environmental Protection Agency, Washington, D.C. 20460
ABSTRACT. This paper presents a groundwater transport model for simulating radionuclide transport in an aquifer, using
an approximate solution of the basic transport equation. The model is designed to avoid (1) relatively high computer simula-
tion costs normally experienced in numerical models and (2) the large errors sometimes introduced when the physical boun-
dary conditions are converted to a mathematical form suitable for the analytical model. The model neglects initially the
effect of radionuclide transport through dispersion and compensates for this effect subsequently with a health effects correc-
tion factor. This correction factor is found to be a function of the Peclet number, a dimensionless parameter expressing the
relative importance of diffusion and convective transportation, and the "transport number," which has been defined and
can be determined by using the parameters of the groundwater transport system. The model has a low cost of simulation and
yet maintains reasonable accuracy of predicting the cumulative radionuclide flowing through a section. This is the primary
output expected from a groundwater transport model for health effects assessments. The model has been integrated into the
PRESTO EPA model designed for the prediction of radiation effects due to a shallow-trench operation.
INTRODUCTION
Comprehensive studies on the evaluation of an op-
timum method of diposing radioactive wastes have
been conducted by various government agencies
(1,2) and by an Interagency Review Group (3). All of
these studies have unanimously concluded that the
geological disposal method is one of the most viable
alternatives. Because the transport of radionuclides
through an aquifer to the biosphere is a primary
pathway, the groundwater transport model, which
simulates the migration of radionuclides in an
aquifer, becomes one of the important submodels re-
quired in a health effects assessment model.
To date, there are more than 108 groundwater
transport models (4) available. However, some of the
models fail to consider the process of radionuclide
decay and/or sorption and, therefore, are not suit-
able for the assessment of a radioactive waste dis-
posal site. The rest of the models, which may be suit-
RECEIVED 12/24/84; ACCEPTED 12/6/85.
Acknowledgements The author is grateful to Mr. G. Lewis
Meyer of EPA for his valuable suggestions and continuous en-
couragement throughout the development of this model. Special
acknowledgements should be made to Dr. Akio Ogata of USGS
and Professor Donald S. Cohen of the California Institute of
Technology for their suggestions and criticisms during the course
of model review.
able for health effects evaluation, can be subdivided
into two groups: the analytical model and the nu-
merical model. In general, the application of an
analytical model is limited by its specific form of
boundary conditions. Therefore, when the actual
boundary conditions do not match the form that the
model called for, some approximation of its actual
boundary conditions would be required before the
analytical solution could be applied. As a result,
these models may suffer from considerable error due
to the approximation of boundary conditions.
The application of a numerical model generally re-
quires many more tedious computations than the
analytical approach. For example, the accuracy of
simulation depends greatly on the adjustments of
time and space increments; severe errors may result if
they are improperly adjusted. On the other hand, a
proper adjustment of these increments may result in
consuming excessive computer time for the simula-
tion, in some cases. Therefore it is conceivable that
the cost of simulation may become prohibitive when
the model is applied to long-term simulations such as
health effect evaluations.
The basic groundwater transport model aiming for
health effects assessment was developed by Hung (8)
and was integrated into the PRESTO-EPA model
(9), a model to predict the radiation effects from
B-3
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42
C. Y. HUNG
shallow trench operation. Since then, the same model
has been improved in theoretical background and in
practical application.
The purpose of this paper is to present the ground-
water transport model used in the PRESTO-EPA
model and its characteristics.
APPLICATION OF EXISTING MODEL IN
HEALTH EFFECTS EVALUATION
The basic equations for a groundwater transport
system include the momentum, the energy, and the
continuity equations for the hydrodynamic system
and for the solute. Using tensor notations, the equa-
tions take the form (10)
(1)
[(Qk/ti)H(Vp - QgVz)} + V p* VT - qL
= (d/dt)[neU + (1 - n)(QCpT)] (2)
v = -(k/n)(Vp - QgVz)
V
Vey_ + cf = -(d/dt)(no)
V . [QC(k//j.)(Vp -
- q-C - Qn\dRC = (d/dt)(enRC),
VC
(3)
(4)
in which C is the concentration of the radionuclide in
the fluid phase; y_ is the velocity vector; k is the
permeability; jj. is the viscosity of the fluid; p is the
pressure; Q is the mass density; g is the gravitational
acceleration; D is the dispersivity tensor; Tis the tem-
perature; qL is the rate of heat loss; H is the fluid en-
thalpy; n is the porosity; z is the height above refer-
ence plane; \d is the radionuclide decay constant; R is
the retardation factor; U is the internal energy; cp is
the specific heat; q' is the rate of fluid withdrawal;
and subscripts h and c are the heat energy and com-
ponent of mass, respectively.
The preceding non-linear equations characterize
the transport of radionuclides in a groundwater sys-
tem. Since each of the preceding equations are re-
lated through dependent variables, the direct solution
of the system equation for any boundary and initial
conditions is extremely difficult. A commonly used
practice in solving the system equation is to assume
that the flow of groundwater is steady and that there
is no heat energy being generated or absorbed in the
system. The system equation then reduces to a single
equation:
R(dC/d() - V (D « VC) + VVC
+ X,/?C = O,
(5)
in which V is the interstitial velocity ( V = V/AJ).
Equation 9 has been further simplified and solved by
numerous investigators (10,11,12, and 13) employing
numerical or analytical approaches. However, some
difficulties are often encountered in applying these
models for health effects assessments. They are de-
scribed in the following sections.
Numerical Models
The existing multidimensional models are solved
either by the finite-difference method (10) or by the
finite-element method (11,12, and 13). A model
employing the finite-element method is, in general,
found to be more efficient than one employing the
finite-difference method (12). However, the time re-
quired to execute a computer model employing the
finite-element method is still far beyond the limita-
tions of a normal project budget for risk assessment
when numerous cases with long durations of simula-
tion must be considered.
Analytical Models
Lester, Jansen, and Burkholder (6) developed an
analytical groundwater transport model for a one-
dimensional, semi-finite aquifer system having im-
pulse release and decaying band release boundary
conditions. These boundary conditions at x = 0 were
expressed as
C = C06(t)
and
C= (C0/Oexp(-Xdt)
(6)
(7)
for the impulse release and the decaying band release,
respectively. In the preceding equation, x is the space
coordinate, t is the time, td is the duration of ra-
dionuclide leaching, and C0 is the concentration of
radionuclides at t 0.
Ford, Bacon, and Davis, Inc. employed an ana-
lytical model that assumed that the rate of radionu-
clide release at any time is proportional to the in-
ventory of radionuclides remaining at the source
point (7). Mathematically, it is expressed as
C = (Xi/m/Q JExp[ - (Xd + \L)t], (8)
in which Xi is the leaching constant, lm is the initial
inventory of the radionuclides in the waste depository,
and Q, is the rate of groundwater flow.
These analytical models have made considerable
contributions in groundwater transport modeling by
simplifying the simulation procedures. However, the
application of these models to health effects assess-
ments is limited, because it requires the approxima-
tion of converting the actual boundary condition to a
form meeting the requirements of the analytical
model. This may result in considerable simulation er-
ror in some cases.
The preceding discussion implies that existing
numerical and analytical groundwater models may
either be too costly to compute or may introduce
large errors when applied to health effect assess-
ments. Therefore, a more accurate and more eco-
nomic groundwater transport model has been devel-
oped for health risk assessments and is presented in
this paper.
B-4
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AN OPTIMUM GROUNDWATER TRANSPORT MODEL
43
THEORETICAL BACKGROUND OF THE
OPTIMUM GROUNDWATER TRANSPORT
MODEL FOR HEALTH EFFECTS
ASSESSMENTS
Derivation of Basic Equation
The groundwater transport model to be discussed
in this section simulates the transport of radionu-
clides from a disposal site to a point where ra-
dionuclides are pumped out to the biosphere for
human uptake or discharged into a surface stream
for another mode of transportation. To simplify the
model, it is assumed that the flow of the fluid carry-
ing the radionuclides is steady, uniform, and one-
dimensional. It is also assumed that the dissolved ra-
dionuclides are in equilibrium with those adsorbed by
the solids in the aquifer formation and that decay is
in progress for both dissolved and absorbed radionu-
clides.
The basic one-dimensional groundwater transport
equation for the model simulating radionuclide
migration in an aquifer may be reduced from Eq. 5 to
D(32C/dx2) - V(3C/3x) - R(dC/dt)
- \,RC = 0
(9)
which is to be solved by the following initial and
boundary conditions:
C = 0, at all x, when t = 0, (10)
C = C0(t), at x = 0, when t < 0, and
C = finite, at x - oo when t > 0.
(11)
For the convenience of analysis, one may transform
the dependent variable from radionuclide concentra-
tion, C, into the rate of radionuclide transport by
multiplying Eqs. 9, 10, and 1 1 by the rate of ground-
water flow. When this transformation is completed,
the preceding equations become:
D(d*Q/dx2) - V(dQ/dx) - R(dQ/dt)
- \dRQ = 0 (12)
Q = 0, at all x, when t = 0,
Q = Q0(t), at x = 0, when t > 0, and (13)
Q = finite, at x - oo when / > 0,
where Q denotes the rate of radionuclide transport.
Since Eq. 13 is an undefined boundary condition,
the analytical solution for Eq. 12 cannot be obtained.
However, one may express its solution into a con-
volution form expressed by:
\'0Qo(t ~ r)u(r)dr, (14)
in which u denotes the radionuclide release rate at the
discharge end and, x = L, which responds to the unit
release of a radionuclide at x = 0 and when T = 0.
This function is normally known as unit response
function.
The preceding unit response function, U(T), has
been thoroughly studied by Burkholder et al. (6),
with the following results:
u(T) = (Y/2LM(RP/ir03) Exp| -
-(PO/4R)[(R/6)-l]2\.
(15)
in which P is the Peclet number (= VL/D); 8 is the
dimensionless time (= rV/L); Nd is the decay
number (= \dL/V). By substituting Equation 15 into
Eq. 14, one obtains:
QW = U Q.(t - r) (V/2L)^f(RP770^)
- (P6/4R)[(R/ff) - IVldr. (16)
Equation 16 cannot be integrated because Q0(t - T)
is undefined. However, if the dispersion term, D(d2Q/
dx2), in Eq. 12 is neglected, then the unit response
function, I/(T), for the modified Eq. 12 becomes (6):
= Exp(-RL\d/V)8(r - RL/V)
(17)
As a consequence, Eq. 14 can be integrated, and the
result is
Q'(t) = Q°(t ~ RL/V)E\p(-\dRL/V).
(18)
In Eqs. 17 and 18, 5 denotes the delta function, and
the prime on i/ and Q' denotes variables responding
to the system with the dispersion term being
neglected.
Although Eq. 18 is easier to calculate than Eq. 16,
the results obtained from Eq. 18 include an error
resulting from neglecting the dispersion term in the
basic transport equation. To compensate for this er-
ror, a correction factor defined by
= Q(t)/Q'(t) (19)
has been introduced. After this correction factor has
been characterized, the rate of radionuclide transport
Q(t) can be obtained by combining Eq. 18 and 19.
The result is:
- RL/ K)Exp( - RL\d/ V).
(20)
In Eq. 20, the correction factor £ is expected to be
a function of /, P, and \dRL/V; the complexity of
this term prohibits its application. This correction
factor is further transformed into time independent
factor based on the ground that the trasport model is
primarily for the purpose of risk assessment. The
transformation is derived as follows:
The assessment of health effects due to direct
and/or indirect ingestion of groundwater contami-
nated with radionuclides involves complicated simu-
lation of the history of organ doses. Such an assess-
ment also requires the probabilistic analysis of the
occurrence of fatal cancer effects following the simu-
lation of radionuclide transport in the acquifer. Due
to the complexity of the dose and health effects simu-
lation, a linear model is generally employed in vari-
B-5
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44
C. Y. HUNG
ous risk assessment models. An example of this ap-
plication is the PRESTO-EPA model (9).
When a linear model is employed, the annual
health effects due to the ingestion of a specific ra-
dionuclide, E,, for a community with a population of
P' can be expressed by (14):
(H.), = (P'/T.) £ £.(*/),...
(21)
in which R, is the health risk conversion factor per
unit rate of chronic ingestion, T, is the number of
years of life expectancy, E is the rate of radionuclide
exposure, and / and 1 denote the order of radionu-
clide and human organs. Furthermore, since a risk
assessment involves the estimates of health effects for
infinite generations residing at the community of in-
terest, the total health effect due to the exposure rate
of E. pCi/yr is calculated by the following generalized
equation:
(H,), = \"(P'/T.) - 2J EUR,),,Idt
1=1
M
= (P'/T.) £ (R/)l,l^E.dt,
1=1
(22)
where H, is the total health effects and t is the time.
Since the annual rate of pumping radionuclides
that will be ingested by humans is directly propor-
tional to the rate of radionuclides being transported
to the wellpoint, one may write:
E, = rQJP
(23)
where r is the ratio of the rates of radioactivity ex-
pected to be uptaken by the inhabitants of the com-
munity to the rate of radioactivity reaching the well-
point, and Q, is the rate of radionuclides being
transported to the wellpoint.
Substituting Eq. 23 to Eq. 22, one obtains
,), = (r/T.)
(24)
Equation 24 indicates that the total health effects de-
pend on the total cumulative activity of radionuclides
reaching the wellpoint and are independent of the
time variation of the transport rate. Therefore, for
the purpose of health effects assessment, the key in-
put required from a groundwater transport model is
the cumulative radionuclides reaching the wellpoint
over an infinite period of time. This is the key con-
cept used in developing the groundwater model
presented in this paper.
Since the goal of health effects assessments is
estimating fatal health effects, one may also intro-
duce a long-term health effects correction factor, 77,
defined by:
r, = //,////, (25)
where H, and H,' represent the total health effects ob-
tained from the groundwater pathway at the discharge
end with and without considering the dispersion
term, respectively.
For the purpose of developing a ground water
transport model, one may assume that the popula-
tion affected by the well water remain constant and
that the total health effects due to the released ra-
dionuclides are so small that they would not alter the
size of the population at risk and the other factors af-
fecting the health effects. If this is the case, there will
be a linear relationship between the cumulative ra-
dionuclides reached at that point and the expected
total health effects. Substituting Eq. 24 into Eq. 25
and lumping together all terms affecting the health
effects conversion factors into a single health effects
conversion factor, then Eq. 25 can be rewritten as:
r, = ((Fk)\:Q(t)dt}/((Fh-)\:Q'(t)dt}. (26)
where Fh denotes the conversion factor for health ef-
fect from cumulative radionuclide release.
Subsequent substitution of Eq. 14 into Eq. 26
yields:
Q0(t - T)u'(T)dTdt. (27)
When the order of integration of the double integral
for both numerator and denominator is reversed, Eq.
27 can be rewritten as:
r> - (
Q0(t -
(28)
Furthermore, when the independent variable, t, is
transformed to a such that a = t T, Eq. 28 becomes
(29)
Since Q0 is independent of T and u and u1 are in-
dependent of a, the double integrals in the denomina-
tor and numerator can now be separated into prod-
ucts of single integrals and yield:
which can be simplied as:
1 = [\'u
-------
AN OPTIMUM GROUNDWATER TRANSPORT MODEL
45
Equation 31 is the basic equation of this groundwater
transport model.
Characterization of Health Effects Correction Factor
To determine the characteristics of the health effects
correction factor, one may first substitute Eqs. 15
and 17 into Eq. 30 and then complete the integration
of the denominator. This yields
- (PO/4R)(R/6 -
Exp(-/?LX,/K)
(32)
The numerator of Eq. 32 can also be integrated into a
modified Bessel function of the second kind (15);
when the result of integration is substituted, Eq. 32
becomes:
Exp I
Exp -
(33)
Equation 33 indicates that the health effect correc-
tion factor is a primary function of the Peclet number
and the parameter expressed by \dRL/V. This pa-
rameter represents the ratio of the radioactive decay
constant, \d, and the "transport constant", V/RL,
and is designated as "transport number" for this
study. The preceding results were plotted on a Peclet
number vs. transport number plane, as shown in Fig.
1 . This figure indicates that the health effects conver-
sion factor, 7), increases with the increase in transport
number and decreases with the increase in Peclet
number. Equation 33 also indicates that the health
effects correction factor is always greater than 1 .
Proposed Groundwater Transport Model for
Health Effects Assessment
Based on the previous discussions, a groundwater
system with initial and boundary conditions as shown
in Eq. 13 may be simulated by Eq. 31, which is dupli-
cated as:
G(0 = 17 Qo(/
Exp(-RL\d/Y). (34)
10,000
8,000
6,000
4,000
2,000
1,000
800
600
400
200
£ 100
| 80
60
50
20
10
A
L
/
LL
fill /I/ I
z
7/
rz
LLUL
77
77
L/LL
LL77/7LI
7_7
LTL
77
Z
/ ,
7
L'l
77
0.1 0.2 0.4 0.60.81 2 4 6 8 10 20 40 6080100
Trtniport Number, XdRL/V
FIGURE 1. Results of health effect collection factor analysis, Equation 33.
B-7
-------
46
C. Y. HUNG
Equation 34 represents an algebraic equation, in
which constant, r;, is determined from Eq. 33; and
the terms RL/V and X, are also known constants
determined from the characteristics of the ground-
water system. Therefore, the proposed model de-
scribed by Eq. 34 is the simplest and most economical
to process when it is integrated into a health effects
assessment model.
It should be noted that when this model is
employed in a health effects assessment model, there
may be a slight error in the health effects for each in-
dividual generation, but the total health effects for
all generations should remain the same as that ob-
tained from the direct integration of Eq. 14. The
nature of this error is characterized in the following
section.
CHARACTERIZATION OF THE POTENTIAL
ERROR OF THE PROPOSED MODEL
Hypothetical Groundwater System
To characterize the nature of error incurred by the
proposed model, a hypothetical groundwater trans-
port system was established. In the hypothetical
groundwater system, it was assumed that: the veloc-
ity of groundwater flow is 100 m/yr; the location of
radionuclide discharge is 500 meters downstream
from the source point where the radionuclide is re-
leased; the coefficient of dispersion is 300 mVyr; the
rate of radionuclide release at the source point, x = 0,
varies with time and is represented by
10
l
II
o:
! i
~ o
1*
800
Rite o( RelUM »t x 0
Result of Analysis. Optimum Model
---- Result of Analysis, Ex»ct Model
FIGURE 2. Comparison of the results of analyses obtained from the Optimum Model and the Exact Model, Case I, X,, = 0.000693,
200 years.
B-8
-------
AN OPTIMUM GROUNDWATER TRANSPORT MODEL
47
Qo(t) = 0
for 0 < / < td
for t > td,
(35)
where td is the duration of radionuclide release.
Three cases are assumed for the analysis. Case I
represents a fast release, td = 200 yr, and long ra-
dionuclide half-life, X, = 0.000693. Case II repre-
sents a fast release, td = 200 yr, and short ra-
dionuclide half-life, X^ = 0.0693. Case III represents
a slower release, td = 400 yr, and long radionuclide
half-life, \d = 0.000693. Each case is also subdivided
into three subcases with the retardation factors equal
to 1, 10, and 100, respectively.
Method and Results of Analysis
Two models were developed for the analysis. One of
them was developed on a numerical integration of
Eq. 16 and was designated as the "Exact Model." The
other model was developed based on Eq. 34 and was
designated as the "Optimum Model." Each of these
models was designed to compute the radionuclide
discharge rate at the downstream end of the aquifer
and the cumulative radionuclides released at the dis-
charging point over infinite time. The results of com-
100
200
300 400 500
Time, yr
600
700
800
Legend:
..... Rate of Release at x - 0
^ Result of Analysis, Optimum Model
- Result of Analysis, Exact Model
FIGURE 3. Comparison of the Results of analyses obtained from the Optimum Model and the Exact Model Case II, X,, = 0.0693, 1,
200 years.
B-9
-------
48
C. Y. HUNG
puter analyses using these two models are presented
in Figs. 2, 3, and 4.
DISCUSSION OF RESULTS
For Cases I and III with long radionuclide half-life,
the rate of radionuclide release and the cumulative
radionuclide release computed from the exact model
and the optimum model agree very well for all three
subcases assumed. However, the results of the Case
II analysis, where the radionuclide half-life is short,
indicate, that the rate of radionuclide discharge ob-
tained from the optimum model deviates more and
more from that obtained from the exact model as the
retardation factor increases. Nevertheless, the major
deviations are merely in the time-lag of radionuclide
discharge, whereas the peak discharge showed little
deviation (Fig. 3). The results of this latter analysis
also indicated that the above deviation will be miti-
gated for those radionuclides with longer half-life;
i.e., with smaller transport number (Fig. 2). Fortu-
nately, a system with larger transport numbers results
in a limited quantity of radionuclide discharge at its
discharging point, as can be seen by comparing case
II-3 with cases II-2 or II-1. This result implies that the
discharge of radionuclides under a high transport
So
O 5
«
cc
S
fl
S i
11
| c
II
oc S
"H
S5
800
Legend:
Rate of Release at x 0
Result of Analysis, Optimum Model
R«ult of Analysis, Exact Modal
FIGURE 4. Comparison of the results of analyses obtained from the Optimum Model and the Exact Model, Case II, X, = 0 000693 t
400 years. ' ' ' '
B-10
-------
AN OPTIMUM GROUNDWATER TRANSPORT MODEL
number, such as Case II-3, would not be a major
concern from the point of view of health effects as-
sessment. Besides, this deviation should further
decrease with the increase in the duration of radionu-
clide release at the radionuclide source point, as
shown in Figs. 2 and 4.
Nevertheless, the cumulative radioactive discharge,
which is the primary parameter in determining total
health effects from a radioactive waste disposal site,
remains the same for those obtained from the exact
model and from the optimum model in all cases. This
agreement implies that the proposed optimum ground-
water transport model can be integrated into the
health effects assessment model without introducing
any significant error in the assessment of health ef-
fects.
APPLICATION TO A RISK
ASSESSMENT MODEL
The optimum groundwater model has been in-
tegrated into the PRESTO-EPA model, a model
designed to predict the radiological effects due to the
disposal of radioactive wastes by a shallow trench
operation. The PRESTO-EPA model is a complete
risk assessment model. It includes the simulation of
radionuclide transport from the wastes through
hydrologic and atmospheric pathways to environ-
mental receptors and from the environmental re-
ceptors to human organs through food-chain path-
ways and the evaluation of fatal health effects from
the history of organ dosimetries. The model was
developed by the Oak Ridge National Laboratory for
EPA.
The groundwater transport submodel receives the
output from the leaching submodel as its boundary
conditions and calculates the rate of radionuclide
transport at the wellpoint. These outputs are then fed
into the food-chain submodels for human exposure
evaluations and, subsequently, for health effects
assessments.
The PRESTO-EPA model has been used to assess
the health effects for over 400 different combinations
of radionuclide source terms with various hydro-
geological, demographical, and disposal conditions.
The model interacts with other submodels smoothly,
implying that the proposed optimum groundwater
transport model can be integrated into a risk assess-
ment model.
CONCLUSION
An optimum groundwater transport model for health
effects assessment has been derived and characterized.
The processing time required to simulate this model
is significantly less than that for other comparable
models, because it requires only algebraic calcula-
tions.
The error from simulating the peak discharge of
radionuclides using the "optimum" model, as com-
pared with the results from that of the "exact" model
(i.e., the numerical model represented by Eq. 16
and 35), may be noticeable when the groundwater
transport number is greater than 5. However, the
cumulative radionuclides released under the same
conditions is normally only a small fraction of the
cumulative radionuclides released at the source
point. Therefore, the effect of this error should not
be as important as that for those radionuclides with
lower transport numbers.
The predicted cumulative radionuclides passing
the point of interest obtained from the proposed "op-
timum" model agree very well with that obtained
from the "exact" model in all cases. This implies that
the proposed model can be integrated into a health
effects assessment model with confidence, if one ac-
cepts a one-dimensional flow model.
The application of the proposed optimum ground-
water transport model to the PRESTO-EPA model
indicated that the model interacts with other sub-
models very smoothly, implying that the model can
be easily integrated into a risk assessment model.
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50
C. Y. HUNG
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simulation in surface and subsurface hydrology. Academic
Press, New York (1977).
13. Yen, G. T. and D. S. Ward. FEMWATER: A finite-element
model of water flow through saturated-unsaturated porous
media. Oak Ridge National Laboratory, ORNL-5567 (1980).
14. Begovich, C. L. et at., DARTAB: A program to combine air-
borne radionuclide environmental exposure data with dosi-
metric and health effect data to generate tabulations of
predicted health impacts. Prepared for the Environmental
Protection Agency, ORNL-5692, (1981).
15. Abramowitz, M. and I. A. Segun. Handbook of mathematical
functions with formulas, graphs, and mathematics tables. Na-
tional Bureau of Standards, Applied Matthematics Series No.
55 (1972).
16. New York State Geological Survey. Computer modeling of ra-
dionuclide migration pathway at a low-level waste burial
ground. West Valley, New York. USEPA (1980).
17. Smith, J. M.; T. W. Fowler, and A. S. Goldin. Environmental
pathway models for evaluating population risks for disposal
of high-level radioactive waste in geologic repositories.
USEPA, 520/5-80-002 (1980).
NOMENCLATURE
C: concentration of radionuclide disolved in fluid.
C0: concentration of radionuclide at t = 0.
cf: specific heat of fluid.
D: dispersivity of fluid.
E: rate of radionuclide exposure.
Fk: fatal health effect conversion factor.
g: acceleration of gravitational force.
H: enthalpy of fluid.
//.: number of fatal health effects.
h: subscript for heat energy.
/: initial inventory of radionuclide.
/': subscript for radionuclide.
k: permeability of porous medium.
L: distance from disposal site to wellpoint.
1: subscript for organs.
M: total number of organs considered.
Nd:
n:
P:
P':
P-
Q-
Q':
Q0:
Qw:
R:
R/.
r.
T:
T.:
t:
td:
U:
u:
V:
v:
x:
z:
d:
r-
d:
decay number ( = Xl/L/P/)-
porosity of porous medium.
Peclet number (= VL/D).
population of community.
intensity of pressure.
rate of radionuclide transport with disperson
effect considered.
tate of radionuclide transport with dispersion
effect neglected.
rate of radionuclide transport at x = 0.
rate of groundwater flow.
rate of fluid withdrawal from the transport
system.
rate of heat loss of fluid.
retardation factor for porous medium.
risk conversion factor.
ratio of radioactivity being uptaken and that
reached the wellpoint.
temperature of fluid.
number of years of life expectancy.
time.
duration of radionuclide leaching.
internal energy.
unit response function with dispersion effects
being considered.
unit response function with dispersion effects
being neglected.
interstitial velocity of groundwater.
velocity vector.
space coordinate in horizontal direction.
height above reference plane.
unit impulse function.
long-term health effects conversion factor.
dimensionless time ( = rV/L).
viscosity of fluid.
radioactive decay constant.
radionuclide leaching factor.
instantaneous radionuclide transport correction
factor.
mass density of fluid.
dummy time variable.
B-12
-------
APPENDIX C
RADE MODEL: RADIOACTIVE ATMOSPHERIC
DISPERSION AND EXPOSURE CODE
C-l
-------
INTRODUCTION
The PRESTO-EPA codeU) for calculating the environmental transport of
nuclides from low-level waste (LLW) disposal facilities, includes a
Gaussian Plume model for atmospheric transport. However, the code only
allows for the calculation of one wind sector, speed, stability, distance
and population to be specified for each PRESTO-EPA calculation. In order
to facilitate the determination of risk elements in the LLW disposal alter-
native risk-cost data matrix, a small program called RADE (Radioactive
Atmospheric ^Dispersion and Exposure) has been written. The RADE code
performs standard Gaussian PTume atmospheric dispersion calculations using
subroutines from PRESTO-EPA. It then performs the Air-Pathway Unit
Response analysis(2) and prepares the output in the form suitable for input
to PRESTO-EPA. This memorandum documents the RADE code and its use to
prepare input to PRESTO-EPA for the following settings:
1) Barnwell, South Carolina
2) West Valley, New York
3) Beatty, Nevada
METHOD OF ANALYSIS
One main objective in developing RADE is to utilize applicable
subroutines in PRESTO-EPA without altering them. The MAIN program collects
and prints out the necessary input data. It then calls the AIRTRM
subroutine for the analysis. AIRTRM in turn calls several support
subroutines. The MAIN program then performs the unit response analysis and
outputs the parameters UEFF, XG, FTWIND, CHIQ and POP parameters for input
into PRESTO.
After the sector-independent data are read in, RADE proceeds through a
DO loop in which the sector-distance data are input, AIRTRM is called and
the key data are accumulated.
The RADE code is organized so that several wind speed distributions,
stability classes or populations within a sector can be included in the
analysis, for this situation, the data for each distribution element are
read in as a new sector. Thus, for example, the sector designation para-
meter, ISEC, can be larger than 16 even though only 16 compass sectors are
used. If the type of stability formation or stability class varies with
the sector-distance designations, then the original source height, read in
Card 2 must be a negative number. The source height for each sector-
distance designation is read from input card set 5B.
The parameters for the community designated as the PRESTO-EPA input
community must be read in last. A complete listing of the RADE code is
given on pages 7-12 .
C-2
-------
AIR CONCENTRATION AS A FUNCTION OF DISTANCE
In order to obtain some insight into the impacts from the atmospheric
dispersion pathway for large populations at large distances from the
facility, RADE2 was used to calculate CHIQ values as a function of distance
for the West Valley meteorological conditions. The results are shown in
Figure 1 for both four and three atmospheric stability conditions. At
large distances both curves in the figure coincide because of the lid
height condition of 300 m used in the calculations.
RESULTS
The air pathway unit response calculations for the three reference
sites are summarized below. The complete RADE output, including the input
data for these sites is given in Appendix B.
Site FTWIND
BarDwell, SC 0.080
West Valley, NY 0.288
Beatty, NV 6.025
POP
111
4,285
50
CHIQ (sec/m3)
1.20E-04
3.25E-07
5.23E-08
When performing the PRESTO calculations the CHIQ is read in so that
subroutine AIRTRM is not called.
c-3
-------
10
X
Q
10
10-7-
100
103 104
DISTANCE (m)
FIGURE 1. CHIQ AS A FUNCTION OF DISTANCE
C-4
105
RAE-100811
-------
FIGURE 1. CHIQ AS A FUNCTION OF DISTANCE
RAE-100811
X
6
10 °-
10-7-
100
103 104
DISTANCE (m) c~5
-------
INPUT SPECIFICATIONS
The input format for RADE is given below:
Card No. Format Parameters
Title Card
H, VG, VD, HLID, ROUGH
CHIQ, RE1, RE2, RES, RR, FTMECH
IT, IS, ISEC
XNAME(J), J = 1,4
H, XG, U, FTWIND, POP
Cards 5A and 5B are repeated for every sector-distance combination
being analyzed.
A description of the input variables is given below.
1
2
3
4
5A
5B
20A4
8F10.0
8F10.0
815
4A4
8F10.0
Variable
H
VG
HLID
ROUGH
CHIQ
RE1
RE2
RES
RR
FTMECH
IT
IS
ISEC
XNAME
XG
U
FTWIND
POP
Description
Source height (m)
Velocity, gravitational fall (m/s)
Lid height (m)
Roughness parameter
1.0
Beginning coefficient in resuspension
equation (not used)
Decay factor in resuspension equation
(not used)
Final coefficient in resuspension equation
(not used)
(not used)
Fraction of year mechanical disturbance
occurs (not used)
Type of stability formulation
1 for PG
2 for Briggs-Smith
Stability class
Number of sector-distance combinations
Community name
Distance to the population in the sector
of interest (m)
Windspeed in the sector of interest
m/s)
Fraction of time the wind blows toward-
the sector of interest
Population at the sector-distance of
interest
C-6
-------
RADE CODES
C RADE
C RADIOACTIVE ATMOSPHERIC DISPERSION AND EXPOSURE.
C INCORPORATES AIRTRM AND RELATED SUBROUTINES FROH PRESTO-EPA.
PROGRAM RADE
COMMON/AIR/H,VG,U fIT.IS,VD,XG.HLID,ROUGH.FTUIND,CHIQ,RE1,RE2,RE3
DIMENSION A(20),XNAME(4)
CALL ASSIGNS,'LA:')
URITE(6,1000)
READ(5,6000) (A(I),1=1.20)
URITE(G,6010) (A(I),I=i.20)
Tl=0.
T2=0.
READ(5,3005) HH.VG,VD.HLID,ROUGH
READ(5,3005) CHI3,RE1,RE2,RE3rRR,FTMECK
READ(5,3010) IT,IS,ISEC
WRITE(G,G400)
WRITECG,G416) ISEC
IF (HH.GE.O.) URITE(fa,6405) HH
WRITE(6.G410) VG
WRITE(6,6420) VD
URITE(b.6435) HLID
WRITE(6,6440) ROUGH
U8ITE(6,6445) IT.IS
URITE(6.6480) REi,RE2,RE3
URITE(6.6500)
DO 1 1=1,ISEC
READ(5,6000) (XNAME(J),J=1,4)
READ(5,3005) XG.U.FTUIND,POP
IFCHH.LT.O.) REAEK5.3010) IT.IS
IFCHH.LT.O.) READ(5,3005) H,VG,VD,HLID.ROUGH
IF(HH.GE.O-) H=HH
C
CALL AIRTRM(EXPOS,DE?0!
r
TO=EXPOSAPOP*FTUIND
T1=T1+TO
T2=T2+POF
WRITE(6.5510) (XNAME(J),J=l.4).XG.U.FTUIND,POP,EXPOS
1 CONTINUE
FTUIND=T1/(PGPAEXPOS)
pT;-)T-T-,
wE!TE(&,5520/
USITE(G.b530) (XNAriEC) ,J=1,4;, XG.U.FTWIND.PDF , EXPOS
WRITE(6,£.540) PTOT
IOCC ;jR^AT'://.lBX.55r^'!./.i8X. r ,53X. ''A' ,/. 1SX. A'.23X.'S A D E .
C-7
-------
S'JSX,'A',/,1SX,'*',53X,'A',/,18X,'A',4X,'RADIOACTIVE ATMOSPHERIC DI
ISPERSION X EXPOSURE',4Xf'A'./,18X,'A'.53X,'AV»13X»55('A'»
3005 FORMAT(8F12.6)
3010 FORMAK8I6)
6000 FORMAT(20A4)
6010 FORMAT(///,1X,20A4,///)
6400 FORMAT(//,20X,'GENERAL INPUT DATA')
6405 EORMAK//.11X, 'SOURCE HEIGHT IS ',FG.l,' METERS')
6410 FORMATdlX,'VELOCITY OF GRAVITATIONAL FALL IS',FG.2,
& ' METERS/SECOND')
6416 FORMATU1X/NO. OF SECTOR DISTANCE COMBINATIONS IS', 14,/, 11X.
X 'ENTER PRESTO REFERENCE POPULATION DATA LAST')
6420 FQRMATU1X,'DEPOSITION VELOCITY IS ',F6.2,' METERS/SECOND')
6435 FORMAT(11X,'LID HEIGHT IS ',F8.2,' METERS')
6440 FORMATU1X/HOSKER ROUGHNESS FACTOR IS ',F6.2)
6445 FORMAT(11X,'TYFE OF STABILITY FORMULATION IS ',I2,/,
& 11X.'STABILITY CLASS IS ',12)
6480 FORMAT(11X,'RESUSPENSION FACTOR PARAMETERS ',3(4X,1PE12.4))
6500 FORMAT'///,3X,'COMMUNITY NAME',7X,'XG',3X,'WIND VELOCITY',4X,
S 'FTWIND',6Xr'POP',llX.'CHIQ',/.24X,'(M)',10X.'(M/SEC>'r26X.
I 'CI/MAA3 PER CI/SEC',/.90('-'),/)
6510 FORMAT(2X,4A4f4XfF7.1,8X,E6.2f8X,F7.5,lXrF8.0,7X,lPE10.3)
6520 FORMAT
END
C
C
r
L<
BLOCK DATA
COMMON/C/BY(6).BZl(6)rBZ2(6),BZ3(6).Al(6),A2(6)?BK6),B2(6),
SB3(6)fPY(6,5).PZ(6,5),QY(6r5)rOZ(6,5).XM(50)
DATA BY/.22,.16,.11,.08,.06,.04/.
& BZ1/.2,.12,.08,.06,.03..016/,
t BZ2/0.,0.,.0002,.0015,.0003,.0003/,
& BZ3/l.,l.,-.5,-.5,-l..-l./
DATA Al/-.0234.-.0147,-.0117.-.0059,-.0059,-.0029/,
S A2/.35f.248,.175,.108..6B8,.054/,
S Bl/.86,-.985,-1.186,-1.35,-2.88,-3.8/,
S B2/-.152,.82,.85,.793,1.255,1.4197,
I B37.1475,.0168,.0045,.0022,-.042,-.0557
DATA PY/.469,.306,.23..219..237..237,0.,.4..36,.32,0.,.31,
I 0..1.7,1.44,.91,1.02,0...66..66,.63,.53,.41,7.56,
S .34,.37..40,.43,.46,7.567
DATA QY/.903..885..855,.764,.691,.594,0.,.91,.36,.78,0...71,
S 0.T. 717. .71, .729, .648,0. ..S3. .83, ,50, .8!)'.. 87, .52.
8, 1.00,.94,.S8,.82,.7&,i.527
DATA PZ/.017,.072..07&,.14,.217,.262,0.,.411,.326,.223.0.,
I .062.0...079..131..91.1.93.0.,.14..14,.21..26,. 13..56,
S .037,.076,.I6..32,nfa6.1.37/
C-8
-------
LifilA U2/1.38,1.021,.879,.727,.61,.5,0.,.907,.859..776,0.,.709,
8 0.,1.2,1.046,.702,.465,0.,1.09,1.09,.98,.89,.83,.55,1.28,
& 1.12..96,.88,.63,.477
DATA XM/1.00.2.00,3.00,4.00,5.00,10.0.15.0,20.0,25.0,30.0,
8 35.0,40.0,45.0,50.0,150.,200.,300.,400.,500.,600.,
I 70Q.,800.,900.,1.E3,1.1E3.1.2E3,1.3E3,1.4E3,1.6E3,1.8E3,
S 2.0E3,2.5E3,3.0E3,3.5E3,4.0E3,4.5E3,5.0E3,6.E3,7.E3,8.E3,
S 1.0E4,1.5E4,2.E4.3.E4,4.E4,5.E4.6.E4,7.E4,8.E4,1.E5/
END
C
C
C
SUBROUTINE AIRTRM(EXPOS,DEPQ)
COMMON/AIF/H,VQ,U,IT,IS,VD.XG,HLID,ROUQH,FTWIND,CHIQ.SE1,RE2,RE3
IF(IS.LT.1.0R.I8.GT.6) WRITE(6r38) IT,IS
IF(IT.EQ.5.AND.(IS.EQ.1.0R.IS.EQ.5» WRITE(6,38) IT,IS
IF(IT.EQ.6.AND.(IS.EQ.1.0R.IS.EQ.6)) URITE(6,38) IT,IS
38 FORMAK2X,'INVALID COMBINATION OF IT=',I2,' AND IS=',I2>
PI=3.141593
IFtHLID.EQ.O.) HLID=12000.
LID=HLID
HH=H-VGAXG/U
IF(HH.LT.O.) HH=0.
C
CALL SIGMAZ(XG. IT, IS,ROUGHSIGZ,IKPM,HLID,VG,U,HH)
C
CQR=1.
IF(VG.EQ.O.O.AND.yn.EQ.O.) GO TO 45
C
CALL DPLT(FI,HH,VD,U,IT,!S,XG,ROUGH,HLID,COR,VG,H>
C
45 EXPO=EXP(-0.5AHHAHH/(SIGZASIGZ >)
EXPN=CORA2.032*EXPO/(SIGZAXG)
EXPOS=EXPN/U
DEPO=EXPOSAVD
80 CONTINUE
RETURN
END
C
C
C
SUBROUTINE DPLTCPI.HH,VD,U.IT,ISfXQ,RQUGH,HLIDfCOR,VQ.H)
DIMENSION XX(50)rEX(50),AX(50)
COMMON/C/BY(6;.BZl(6),BZ2(fa),BZ3(6),Al(6).A2(6).BK6),B2(b),
&B3(b>fPY(b.5),PZ(G.5),QY(6,5J,GZ(6.5),Xh(50)
IEdS.GT.6) IS=6
IKPH-1
IDUM=1
f
L/
C ALL S Ii3MAZ (XG. II, IS, ROUGH, 3 IGZ, IKPM, HL ID, VG, U, HH )
C-9
-------
IKPM=IKPH+1
SQRTP1=0.79785
FX (IKP) =EXP (-0. 5AHHAHH/ (SIGZASIGZ)) ,'S IGZ
XX(IKP)=XG
DO 20 I=1,IKPM
XX(I)=XM(I)
C
CALL SIGMAZ(XX(I),IT.IS,ROUGH,SIGZ,IDUM,HLID,VG.U,HH)
C
FX(I)=EXP(-0.5AHHAHH/(SIGZASIGZ))/SIGZ
20 CONTINUE
L=l
C
CALL SIMPUN(XX,FX,IKP,L.AX)
C
COR=EXP(-SQRTPIAVDAAX(IKP)/U)
RETURN
END
C
C
C
SUBROUIINE SIGMAZ(XG,IT,IS.ROUGH,SIGZ,IKPM,HLID,VG,U,HH)
COMMON/'C/BY(6),BZ1(&),BZ2(&),BZ3(G>,A1(&),A2(&),B1(GJ,B2(6>,
&B3(&),PY(&,5),PZ(&,5),QY(6,5J,QZ(6,5),Xh(50)
DIMENSION AONE(&),BONE(6),ATUO(&>fBTWO(fa),CONE(6).DONE(G),
8CTUO(G),DTUOCG)JW3H(6)
DATA AONE/0.112,0.130,0.112,0.098,0.0609,O.OG38/
DATA BONE/1.06,0.950,0.920,0.889,0.895,0.783/
DATA ATUO/5.38E-4,6.52E-4,9.05E-4,1.35E-3.1.9&E-3.1.36E-3/
DATA BTUO/0.815,0.750,0.718,0.688,0.684,0.672/
DATA CONE/1.56,2.02,2.72,5.16,7.37,11.7/
DATA DONE/0.0480,0.0269,6.,-0.060,-0.0957,-0.128/
DATA CTUO/6.25E-4.7.76E-4,0..186..4290..45900./
DATA DIUO/0.45,0.37,0.,-0.225,-0.60,-0.78/
DATA RGH/0.01,0.04,0.10.0.40,1.0,4.O/
P=0n
BO 8 1=1,50
IKP=I
IF(XHd).GE.XG) GO TO 9
8 CONTINUE
9 IECIKP.LT.2) IKP=2
IKPM=IKP-1
IPOINT=IT
IFCIT.GT.3} IPOINI=4
GO TO (10,20,30,40) IPO INT
10 ALX=ALOG(XG)
SIGZ=EXP(B1(IS)+(B2(IS)+B3(IS)AALX)AALX)/:.15
^Q jn go
20 ABS=ROUGH
CI^YLAG(ABB.RGH.CONE.0.3,6,0)
D1=YLAGCAB3.RGH,DONE.G,2.£,05
C-10
-------
Uii= I Lftij (. fltfb , KljH , LIWU , 0 , 'J , b , 0 )
D2=YLAG(ABS,RGH,DTUOrO,2,6,0>
G=AONE( IS)AXGAABONE< IS)/(1.+ATUO( IS)AXGAABTUO( IS) )
F=ALOG(F)
IFCROUGH.LE.0.10) GO TO 26
F=F+ALOG ( 1 . +1 ./(C2AXGAAD2) )
GO TO 27
26 E=F-ALQG<1.+C2AXGAAD2)
27 SIGZ=GAF
IF(SIGZ.LI.l.) SIGZ=1.
GO TO 99
30 SIGZ=BZ1
GO TO 99
40 2=11-3
SIGZ=PZ(IS,J)AXGAAQZ(IS,J)
99 SIGCAL=2.A(HLID-0.5AHH)/2.15
IF(SIGZ.LT.SIGCAL) GO TO 1000
SIGZ=SIGCAL
1000 RETURN
END
r
w
C
c
SUBROUTINE SIMPUN(XX,FX,NX, I,AX>
DIMENSION XX(2),FX(2).AX(2)
IF(I.LT.O) GO TO 30
AX(1)=0.
DO 10 IX=2,NX,2
D1=XX(IX)-XX(IX-1)
AX(IX)=AX(IX-1)+0.5AD1A(FX(IX)+FX(IX-D)
IF(NX.EQ.IX) GO TO 20
D2=XX(IX+1)-XX(IX-1>
D3=D2/D1
A2=D3/6 - AD2AD2/ ( XX ( IX+ 1 5 -XX ( IX ) )
A3=0.5AD2-A2/D3
10 AX(IX+1)=AX(IX-1)+(D2-A2-A3)AFX(IX-1)+A2AEX(IX)+A3AFX(IX+1)
20 RETURN
30 AX(NX)=0.
DO 40 IX=2,NX,2
IC=NX+1-IX
D1=XX(IC+1)-XX(IC)
AX(IC)=AX(IC+1)+0.5AD1*(FX(IC+1)+EX(IC))
IF(NX.EQ.IX) GO TO 20
D2=XX(IC+1)-XX(IC-1)
D3=D2/(XX(IC)-XX(IC-D)
A2=D3AD2AD2/(6.AD1)
A3=0.5AD2-A2/D3
40 AX(IC-l)=AX(IC+l) + aC-A2-A3)AFX(IC-l)+A2AFX(IC)+A3AFX(IC-^l)
RETURN
END
C-ll
-------
c
c
c
FUNCTION YLAG(XI.X,Y,IND1,N1,IMAX,IEX)
DIMENSION X(1),Y<1)
IND=IND1
N=N1
IEX=0
IF(N.LE.IMAX) GO TO 10
N=IHAX
IEX=N
10 IF(IND.GT.O) GO TO 40
HO 20 J=lrIMAX
IF(XI-X(J)) 30,130,20
20 CONTINUE
IEX=1
GO TO 70
30 IND=J
40 IF(IND.GT.l) GO TO 50
IEX=-1
50 INL=IND-(N+l)/2
IF(INL.GT.O) GO TO 60
INL=1
60 INU=INL+N-1
IF(INU.LE.IMAX) GO TO 80
70 INL=IMAX-N+1
:NU=IMAX
80 5=0.
p=l.
no no J=INL,INU
P=FA(XI-X(J))
D=l.
HO 100 I=INL.INU
IF(I.NE.J) GO TO 90
XD=XI
GO TO 100
90 XD=X(J)
100 D=DA(XD-X(D)
110 S=S+Y(J)/D
YLAG^SAP
120 RETURN
130 YLAG=Y(J)
GO TC 120
END
C-12
-------
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
A
A
A
A
A
R A D E
RADIOACTIVE ATMOSPHERIC DISPERSION 2 EXPOSURE
A
A
A
A
A
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
B E A T T Y
GENERAL INPUT DATA
NO. OF SECTOR DISTANCE COMBINATIONS IS 6
ENTER PRESTO REFERENCE POPULATION DATA LAST
SOURCE HEIGHT IS 1.0 METERS
VELOCITY OF GRAVITATIONAL FALL IS 0.03 METERS/SECOND
DEPOSITION VELOCITY IS 0.03 METERS/SECOND
LID HEIGHT IS 300.00 METERS
HOSKER ROUGHNESS FACTOR IS 0.01
TYPE OF STABILITY FORMULATION IS 1
STABILITY CLASS IS 4
RESUSPENSION FACTOR PARAMETERS l.OOOOE-04 -1.5000E-01
l.OOOOE-09
COMMUNITY NAME
BEATTY
DEATH VALLEY
DEATH VALLEY JN.
LATHROY WELLS
PAHRUMP
FARM VILLAGE
XG
CM)
17000.0
40000.0
58000.0
29000.0
87000.0
29000.0
WIND VELOCITY
(M/SEC)
4.80
4.80
4. SO
4.80
4.80
4.80
FTWIND
0.09000
0.17000
0.11000
0.25000
0.25000
0.25000
POP CHIQ
CI/MAA3 PER C I/SEC
900.
25.
30.
250.
1000.
50.
S.923E-08
3.792E-08
2.615E-G8
5.231E-08
1.744E-08
5.231E-08
PRESTO INPUT
FARM VILLAGE
29000.0
4.30
6.02439
5.231E-OS
AIR PATHWAY POPULATION IS
C-13
-------
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
A
A
A
A
A
R A D E
RADIOACTIVE ATMOSPHERIC DISPERSION X EXPOSURE
A
A
A
A
A
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
BARNUELL
GENERAL INPUT DATA
NO. OF SECTOR DISTANCE COMBINATIONS IS 7
ENTER PRESTO REFERENCE POPULATION DATA LAST
SOURCE HEIGHT IS 1.0 METERS
VELOCITY OF GRAVITATIONAL FALL IS 0.10 METERS/SECOND
DEPOSITION VELOCITY IS 0.10 METERS/SECOND
LID HEIGHT IS 300.00 METERS
HOSKER ROUGHNESS FACTOR IS 0.01
TYPE OF STABILITY FORMULATION IS 1
STABILITY CLASS IS 4
RESUSPENSION FACTOR PARAMETERS l.OOOOE-06 -1.5000E-01
l.OOOOE-11
COMMUNITY NAME
BARNUELL CITY
BLACKVILLE
UILLISTON
ELKO
HILDA
KLINE
3NELLING
XG
(M)
8050.0
21900.0
1S200.0
16400.0
20300.0
16700.0
480.0
WIND VELOCITY
(M/SEC)
2.01
2.01
2.01
2.01
2.01
2. ,01
2.01
FTUIND
0.09000
0.05000
0.02000
0.03000
0.06000
0.05000
0.05000
POP
5572.
2840.
3173.
qoq
!_' XJ - »
ncrrr
OlJvJ B
3i D B
in.
CHIO
CI/MAA3 PER C I/SEC
S.968E-07
1.654E-Q7
1.990E-07
2.209E-07
1 ^C^T fW
1 / u %J C V i
2.169E-07
1.20IE-04
PRESTO INPUT
SMELLING
480.0
,07962
111,
« n *" ? i-
i L' i H L
PATHWAY POPULATION IS 12695.
C-14
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AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
A A
A R A D E A
A A
A RADIOACTIVE ATMOSPHERIC DISPERSION I EXPOSURE A
* A
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
WEST
VALLEY
GENERAL INPUT DATA
NO. OF SECTOR DISTANCE COMBINATIONS IS 33
ENTER PRESTO REFERENCE POPULATION DATA LAST
SOURCE HEIGHT IS 1.0 METERS
VELOCITY OF GRAVITATIONAL FALL IS 0.01 METERS/SECOND
DEPOSITION VELOCITY IS 0.01 METERS/SECOND
LID HEIGHT IS 300.00 METERS
HOSKER ROUGHNESS FACTOR IS 0.01
TYPE OF STABILITY FORMULATION
STABILITY CLASS IS 4
RESUSPENSION FACTOR PARAMETERS
IS 1
l.OOOOE-06
-1.5000E-01
l.OOOOE-10
COMMUNITY NAME
XG
(M)
WIND VELOCITY
(M/SEC)
FTWIND
POP
CHIQ
CI/MAA3 PER C I/SEC
GLENUOOD
CHAFFEE
PROTECTION
SANDUSKY
ELTON
FARMERSVILLE
HUMPHREY C.
HUMPHREY
19300.0
19300.0
21700.0
22500.0
17700.0
23300.0
25700.0
2R200.0
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
0.07170
0.08670
0.08670
0.06380
0.10650
0.09370
0.04860
100
100
100
500
50
978
20
7.545E-OS
7.545E-08
6."HE-OS
6.472E-08
S.227E-08
6.250E-OS
5.666E-08
C-15
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SUGARTOWN
GREAT VALLEY
MARSHFIELD
LANGFORD
NEW OREGON
BOSTON
GOLDEN
GOUANDA
CATTARANGUS
ELLICQTTVILLE
ARCADE
ERANKLINVILLE
RICEVILLE
WEST VALLEY
ASHFORD VALLEY
EAST CONCORD
SARDINIA
YORKSHIRE
LIHE LAKE
h'ACHIAS
ASHFORD
EAST OTTO
OTTO
COLLINS CENTER
SPRINGY ILLE
23300.0
25700.0
19300.0
22500.0
19300.0
20900.0
21700.0
23300.0
21700.0
19300.0
20900.0
20100.0
2400.0
5630.0
5630.0
11300.0
15300.0
17200.0
14500.0
12900.0
14500.0
11300.0
18500.0
17700.0
7420.0
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5. .00
0.04270
0.04270
0.08890
0.08890
0.08890
0.06490
0.07170
0.02500
0.01320
0.04270
0.08670
0.06530
0.09370
0.04860
0.01320
0.04270
0.08670
0.08670
0.10650
0.06380
0.04270
0.01320
0.01320
0-04990
0.07170
150.
2014.
100.
100.
100.
7687.
3128.
2712..
1200.
1677.
3714.
3102.
30.
600.
100.
8171.
2792.
3620.
1191.
2058.
1922.
942.
828.
5037.
4285.
6.250E-08
5.666E-08
7.545E-06
6.472E-03
7.545E-08
6.968E-08
6.711E-08
6.250E-08
6.711E-08
7.545E-08
6.968E-08
7.245E-08
2.565E-06
5.392E-07
5.392E-07
1.504E-07
9.518E-08
8.467E-08
1.004E-07
1.180E-07
1.004E-07
1.504E-07
7.S72E-OS
S.227E-08
3.252E-07
PRESTO INPUT
SPRINGVILLE
7420.0
5.00
0.28829
TOTAL AIR PATHWAY POPULATION IS 59638.
C-16
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REFERENCES
1. C. Little, et al., "PRESTO-EPA: A Low-Level Radioactive Waste
Environmental Transport and Risk Assessment CodeMethodology and
User's Manual," EPA Report (in print).
2. C.Y. Hung, et al., "Use of PRESTO-EPA Model in Assessing Health Effects
From Land Disposal of LLW to Support EPA's Environmental Standards,"
Presented at the 5th Annual DOE LLW participants Information Meeting,
Denver, Colorado, August 30 - September 1, 1983.
*U.S. Government Printing Office
1988 516-002/80061
C-17
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